This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 6 Applications Of Derivatives – Quiz 3 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 6 Applications Of Derivatives Quiz 3 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. What is the absolute maximum value of the function f(x) = $4x^2 + 4x-35$ A) -36. B) -35. C) 13. D) 12. Show Answer Correct Answer: C) 13. 2. If a function has a first derivative that is negative, what does that tell you? A) The function is Concave up. B) The function is increasing. C) The function is decreasing. D) The function is Concave dwon. Show Answer Correct Answer: C) The function is decreasing. 3. It is a conditional concept that can be transformed into an equation which is a part of an optimization problem. A) Concept equation. B) Constraint equation. C) Conditional equation. D) Optimization equation. Show Answer Correct Answer: B) Constraint equation. 4. The population of a town x years after 2000 is modeled by P(x). What is the best interpretation of P'(10) = 50. A) In 2010, the population was increasing 50 people per year. B) The average change in population over the 10 years was 50 people per year. C) It took 10 years for the population to increase by 50 people. D) In 2010, the population was 50 people. Show Answer Correct Answer: A) In 2010, the population was increasing 50 people per year. 5. Find the second derivative of f(x) = x$^{2 }$+ e$^{x }$-cosx A) F"(x) = 2x + e$^{x}$ + cosx. B) F"(x) = 2x + xe$^{x}$-cosx. C) F"(x) = 2x + e$^{x}$ + sinx. D) F"(x) = 2 + e$^{x}$ + cosx. Show Answer Correct Answer: D) F"(x) = 2 + e$^{x}$ + cosx. 6. How many critical numbers does f have if $f'\left(x\right)=(x-2)^2(x+5)$ A) 3. B) 0. C) 2. D) 1. Show Answer Correct Answer: C) 2. 7. If total cost C(x)=2x$^{2}$ + 10x + 50, find MC(x). A) 4x$^{2}$ + 10. B) 2x + 10. C) 2x$^{2}$ + 10x. D) 4x + 10. Show Answer Correct Answer: D) 4x + 10. 8. What is a point of inflection? A) When a function goes from increasing to decreasing. B) When a function goes from concave up to concave down. C) All the above. D) None of the above. Show Answer Correct Answer: B) When a function goes from concave up to concave down. 9. What is the maximum value of f(x) = x$^{3}$-3x$^{2}$-1 on the interval [-3, 2]?$_{}$ A) 5. B) 2. C) 0. D) -1. Show Answer Correct Answer: D) -1. 10. For what value of c is the Rolle's thm applicable on the given function f(x) = x$^{2}$-5x+4 [1, 4] A) C = 9/2. B) C = 3/2. C) C = 5/2. D) C = 7/2. Show Answer Correct Answer: C) C = 5/2. 11. The point on the curve $y^2=4x$ A) $\left(1, 2\sqrt{2}\right)$. B) $\left(1, -2\right)$. C) $\left(1, 2\right)$. D) $\left(-2, 1\right)$. Show Answer Correct Answer: C) $\left(1, 2\right)$. 12. A triangular trough is 10 ft long, 6 ft wide across the top, and 3 ft deep. If water flows in the rate of 12 ft/min, find how fast the surface is rising when the water is 6 inches deep? A) 2.2 ft/min. B) 1.2 ft/min. C) 1.8 ft/min. D) 1.5 ft/min. Show Answer Correct Answer: B) 1.2 ft/min. 13. Find the derivative of f(x) = x$^{2}$sinx A) F'(x) = 2xsinx + x$^{2}$cosx. B) F'(x) = 2xcosx. C) F'(x) = 2xsinx + x$^{2}$sinx. D) F'(x) = 2xsinx-x$^{2}$cosx. Show Answer Correct Answer: A) F'(x) = 2xsinx + x$^{2}$cosx. 14. If $f\left(x\right)=\sin\left(\frac{x}{2}\right), $ $c$ $\frac{\pi}{2} A) $\pi$. B) $\frac{3\pi}{4}$. C) $\frac{2\pi}{3}$. D) $\frac{5\pi}{6}$. Show Answer Correct Answer: A) $\pi$. 15. What's the difference between Rolle's Theorem and the Mean Value Theorem? A) Just the name. B) The Mean Value Theorem tests for global maxima/minima, Rolle's Theorem only finds local maxima/minima. C) Rolle's Theorem doesn't require the function to be differentiable. D) The Mean Value Theorem is a stronger version of Rolle's Theorem. Show Answer Correct Answer: D) The Mean Value Theorem is a stronger version of Rolle's Theorem. 16. For a function g(x), g" (3)=-8 indicates that g(x) is ..... at x=3. A) Concave down. B) Decreasing. C) Increasing. D) Concave up. Show Answer Correct Answer: A) Concave down. 17. Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the angle between the tip of the ladder and the house changing when the ladder is 5 ft high? Hint:Use a trig function. A) .6 deg/sec. B) The angle is not changing. C) -.5 deg/sec. D) 1 deg/sec. Show Answer Correct Answer: A) .6 deg/sec. 18. Find the fourth derivative of the following functions with respect to x. $y=3x^2+5x-1$ A) 0. B) $3x+5$. C) $6$. D) $5$. E) $6x+5$. Show Answer Correct Answer: A) 0. 19. A light is placed on the ground 30 ft from a building. A man 6 ft tall walks from the light toward the building at the rate of 5 ft/sec. Find the rate at which the length of his shadow is changing when he is 15 ft from the building. A) -3 ft/sec. B) -6 ft/sec. C) -5 ft/sec. D) -4 ft/sec. Show Answer Correct Answer: D) -4 ft/sec. 20. Which of the following is the absolute maximum value of the function y = x$^{3}$-3x$^{2}$-1 on the given interval [-1, 4]? A) 49. B) 15. C) 5. D) -1. Show Answer Correct Answer: B) 15. 21. A function is what if its second derivative is positive? A) Concave down. B) Decreasing. C) Concave up. D) Increasing. Show Answer Correct Answer: C) Concave up. 22. If the total cost function of producing x units of a commodity is given by $360-12x+2x^2$ A) 6. B) 3. C) 24. D) 12. Show Answer Correct Answer: B) 3. 23. What is a vertical tangent? A) Has a negative slope. B) Has a slope of zero. C) Has an undefined slope. D) Has a positive slope. Show Answer Correct Answer: C) Has an undefined slope. 24. When f'(x) changes from positive to negative at a Critical Value, then there is ..... A) A maximum. B) A minimum. C) No extrema. D) None of the above. Show Answer Correct Answer: A) A maximum. 25. Which of the following is the absolute minimum point of the function y = x$^{3}$+ 6x$^{2}$-12 on the given interval [-2, 5]? A) (0, -12). B) (-2, 4). C) (-4, 20). D) (5, 263). Show Answer Correct Answer: A) (0, -12). 26. A particle has positive velocity if it's position graph is A) Negative. B) Positive. C) Decreasing. D) Increasing. Show Answer Correct Answer: D) Increasing. 27. What is the linearization function L(x) for y = (2x-1)$^{2 }$for values of x near 3? A) L(x) = 20x-35. B) L(x) =-4x + 1. C) L(x) = 4(2x-1). D) L(x) = (2x-1)$^{2}$ (x-3). Show Answer Correct Answer: A) L(x) = 20x-35. 28. Find dy/dxxy+y$^{2}$=2 A) -3x/y. B) Y/(x+2y). C) -3y/x. D) -y/(x+2y). Show Answer Correct Answer: D) -y/(x+2y). 29. Let L(x) = 3(x-4)-2. Find L(3.9). A) 1. B) -2.3. C) -1.7. D) 2.3. Show Answer Correct Answer: B) -2.3. 30. Find the derivative of the function:$g\left(t\right)=\tan\left(\cos4t\right)$ A) $g'=-4\sin4t\sec^2\left(\cos4t\right)$. B) $g'=\sin4t\sec^2\left(\cos4t\right)$. C) $g'=-\sin4t\sec^2\left(\cos4t\right)$. D) $g'=4\\sin4t\sec^2\left(\cos4t\right)$. Show Answer Correct Answer: A) $g'=-4\sin4t\sec^2\left(\cos4t\right)$. 31. Evaluate the limit. $\lim_{x\rightarrow2}\\frac{x^2-4x+4}{x^3-12x+16}$ A) 6. B) 4. C) $\frac{1}{6}$. D) $\frac{1}{4}$. Show Answer Correct Answer: C) $\frac{1}{6}$. 32. Marginal profit is equal to: A) D$^{2}$R/dx$^{2}$. B) R(x)-C(x). C) (R(x)-C(x))/x. D) DR/dx-dC/dx. Show Answer Correct Answer: D) DR/dx-dC/dx. 33. For a function f(x), f" (4)=0 indicates that x=4 is ..... A) A critical point. B) An inflection point. C) A relative minimum. D) A relative maximum. Show Answer Correct Answer: B) An inflection point. 34. Which if the following is not a correct notation for 'derivative?' A) X'. B) F'(x). C) Y'. D) Dy/dx. Show Answer Correct Answer: A) X'. 35. Find dy for the function y = 4x$^{2 }$+ x + 3. A) (4x + 1)dx. B) (8x$^{2 }$+ x + 3)dx. C) 8x + 1. D) (8x + 1)dx. Show Answer Correct Answer: D) (8x + 1)dx. 36. Where does the function, f(x) = 2x$^{3}$-9x$^{2 }$+ 12x-3 have relative max/min values? A) Rel max x =-1, Rel min x = 2. B) Rel max x = 1, Rel min x = 2. C) Rel min x = 1, Rel min x = 2. D) Rel max x = 2, Rel min x = 1. Show Answer Correct Answer: B) Rel max x = 1, Rel min x = 2. 37. If $f'\left(x\right)=\frac{1}{1+x^2}$ $g'\left(x\right)=\frac{1}{\left(1+\frac{x^2}{4}\right)}\cdot\frac{1}{2}$ $x, $ $\lim_{x\rightarrow0}f\left(x\right)=\lim_{x\rightarrow0}g\left(x\right)=0, $ $\lim_{x\rightarrow0}\\frac{f\left(x\right)}{g\left(x\right)}=$ A) 0. B) $\frac{1}{2}$. C) 2. D) 1. Show Answer Correct Answer: C) 2. 38. A kite is 40 ft high with 50 ft cord out. If the kite moves horizontally at 5 miles per hour directly away from the boy flying it, how fast is the cord being paid out? A) 4.2 ft/sec. B) 4.4 ft/sec. C) 4.3 ft/sec. D) 4.1 ft/sec. Show Answer Correct Answer: B) 4.4 ft/sec. 39. What is the lowest point on a function called? A) Relative maximum. B) Absolute minimum. C) Absolute maximum. D) Relative minimum. Show Answer Correct Answer: B) Absolute minimum. 40. Find the given integral:$\int_{ }^{ }\left(x^3-3x\right)dx$ A) $\frac{x^4}{4}-\frac{3x^2}{2}+C$. B) $\frac{x^4}{4}-3x+C$. C) $\frac{x^4}{3}-3x^2+C$. D) $3x^2-3+C$. E) $4x^4-6x^2+C$. Show Answer Correct Answer: A) $\frac{x^4}{4}-\frac{3x^2}{2}+C$. 41. What is the equation of the normal line at x =-3 of $y=x^2+12x+11$ A) $y-16=6\left(x-3\right)$. B) $y-16=-2\left(x-3\right)$. C) $y+16=6\left(x+3\right)$. D) $y+16=6\left(x-3\right)$. Show Answer Correct Answer: C) $y+16=6\left(x+3\right)$. 42. Water is flowing into a spherical tank with 6 foot radius at the constant rate of $30\pi$ $V=\frac{\pi h^2}{3}\left(18-h\right).$ A) 1.0 ft per hr. B) 0.5 ft per hr. C) 1.5 ft per hr. D) 2.0 ft per hr. Show Answer Correct Answer: C) 1.5 ft per hr. 43. A function is increasing if its first derivative is what? A) Zero. B) Negative. C) Undefined. D) Positive. Show Answer Correct Answer: D) Positive. 44. What will be true at an inflection point? A) The function is undefined. B) F ''(x)=0. C) F(x)=0. D) F'(x)=0. Show Answer Correct Answer: B) F ''(x)=0. 45. Is your approximation in #14 an under or over approximation? A) Exact. B) Over. C) Neither. D) Under. Show Answer Correct Answer: B) Over. 46. If (a, b) is a local MAXIMUM on f (x), then what will be true about f '' (a)? A) It's zero. B) It's positive. C) It's negative. D) Cannot be determined. Show Answer Correct Answer: C) It's negative. 47. For times t > 0, a particle moves on the x axis with its acceleration defined by a(t) = 6t-2. If the velocity of the particle is-7 at t = 1, then at what time is the particle at rest? A) T = 4. B) T = 2. C) T = 4/3. D) T = 1. Show Answer Correct Answer: B) T = 2. 48. Derive y=e$^{3x}$ A) 3xe$^{3x}$. B) E$^{3x}$. C) 3e$^{3x}$. D) 3x. Show Answer Correct Answer: C) 3e$^{3x}$. 49. These are word problems that deal with the application of maximum and minimum value of a function. A) Maximizing and Minimizing Problems. B) Optimization Problems. C) Pogi Problems. D) Application Problems. Show Answer Correct Answer: B) Optimization Problems. 50. Let y = x$^{3 }$Find the differential when x =2 and dx = 0.1. A) 0.1. B) 1.1. C) .12. D) 1.2. Show Answer Correct Answer: D) 1.2. 51. If f "(x) >0, what is true about f(x)?Note:you are given the second derivative. A) It has an inflection point. B) It is concave down at that point. C) It is concave up at that point. D) It's zero. Show Answer Correct Answer: C) It is concave up at that point. 52. If a cone of maximum volume is inscribed in a given sphere, then the ratio of the height of the cone to the diameter of the sphere is A) 1/4. B) 2/3. C) 1/3. D) 3/4. Show Answer Correct Answer: B) 2/3. 53. What values separate intervals of increasing and decreasing? A) Possible points of inflection. B) Critical numbers. C) All the above. D) None of the above. Show Answer Correct Answer: B) Critical numbers. 54. Projectiles on Earth follow parabolic trajectories. What would have to be true in order for projectiles to follow cubic trajectories? A) Acceleration due to gravity is constant no matter the distance from the center of Earth. B) Acceleration due to gravity is $0$. C) Earth has no gravitational field. D) Acceleration due to gravity is linear with respect to distance from the center of Earth. Show Answer Correct Answer: D) Acceleration due to gravity is linear with respect to distance from the center of Earth. 55. Evaluate:$\int_0^3\left(x+1\right)^{\frac{1}{2}}dx$ A) $\frac{16}{3}$. B) $\frac{21}{2}$. C) $7$. D) $-\frac{1}{4}$. E) $\frac{14}{3}$. Show Answer Correct Answer: E) $\frac{14}{3}$. 56. We want to construct a box whose base length is 3 times the base width. If the box must have a volume of 50 ft$^{3}$, determine the dimensions that will minimize the amount of material used. A) W=0.485ft, h=2.111ft, l=4.222ft. B) W=1.488ft, h=3.347ft, l=6.694ft. C) W=2.231ft, h=3.347ft, l=6.694ft. D) W=2.027ft, h=4.055ft, l=6.082ft. Show Answer Correct Answer: C) W=2.231ft, h=3.347ft, l=6.694ft. 57. Differentiate (2x + 2)(x-5)$^{8}$ with respect to x. A) 2(x-5)$^{8}$. B) 16(x-5)$^{7}$. C) 8(2x + 2)(x-5)$^{7}$ + 2(x-5)$^{8}$. D) (2x + 2)(x-5)$^{7}$ + 2(x-5)$^{8}$. Show Answer Correct Answer: C) 8(2x + 2)(x-5)$^{7}$ + 2(x-5)$^{8}$. 58. Let $f\left(x\right)=x^4+ax^2+b, $ $x=1.$ A) A = 1 and b =-6. B) A = 1 and b = 6. C) A =-6 and b = 5. D) A =-6 and b = 1. Show Answer Correct Answer: D) A =-6 and b = 1. 59. A function is what if its second derivative is negative? A) Increasing. B) Decreasing. C) Concave up. D) Concave down. Show Answer Correct Answer: D) Concave down. 60. If (a, b) is a local minimum, then what will be true about f'(a)? A) It's positive. B) It's zero. C) It's negative. D) Cannot be determined. Show Answer Correct Answer: B) It's zero. ← PreviousNext →Related QuizzesScience QuizzesClass 12 QuizzesClass 12 Mathematics Chapter 6 Applications Of Derivatives Quiz 1Class 12 Mathematics Chapter 6 Applications Of Derivatives Quiz 2Class 12 Mathematics Chapter 6 Applications Of Derivatives Quiz 4Class 12 Mathematics Chapter 1 Relations And Functions QuizClass 12 Mathematics Chapter 10 Vector Algebra QuizClass 12 Mathematics Chapter 11 Three Dimensional Geometry QuizClass 12 Mathematics Chapter 12 Linear Programming QuizClass 12 Mathematics Chapter 13 Probability Quiz 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books