This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 6 Applications Of Derivatives – Quiz 2 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 6 Applications Of Derivatives Quiz 2 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. The function f is twice differentiable with f(2) = 1, f'(2)=4, and f" (2)=3. What is the value of the approximation of f(1.9) using the line tangent to the graph of f at x = 2? A) 1.4. B) 0.4. C) 0.7. D) 0.6. Show Answer Correct Answer: D) 0.6. 2. If the graphs of the marginal cost and marginal revenuefunctions C'(q) and R'(q) cross at q*, then marginal revenue is equal to marginal cost at q*. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 3. Given a function, f(x), if f'(x)>0 over a certain interval, then f(x) is ..... over that interval. A) Concave down. B) Concave up. C) Increasing. D) Decreasing. Show Answer Correct Answer: C) Increasing. 4. A ladder 10 ft long is leaning against a wall. If the bottom of the ladder is pulled away from the wall at a rate of 2 ft/s, how fast is the top of the ladder sliding down the wall when the bottom is 6 ft from the wall? A) 1 ft/s. B) 3 ft/s. C) 1.5 ft/s. D) 2 ft/s. Show Answer Correct Answer: C) 1.5 ft/s. 5. . What is the nature of function f(x) = 7x-4 on R? A) Increasing. B) Decreasing. C) Strictly Increasing. D) Increasing and Decreasing. Show Answer Correct Answer: C) Strictly Increasing. 6. Find the given integral:$\int_{ }^{ }\cos\left(2x+3\right)dx$ A) $\sin\left(2x+3\right)+C$. B) $\frac{1}{2}\sin\left(2x+3\right)+C$. C) $2\sin\left(2x+3\right)+C$. D) $-\sin\left(2x+3\right)+C$. Show Answer Correct Answer: B) $\frac{1}{2}\sin\left(2x+3\right)+C$. 7. Find $\frac{dy}{dx}$ $y^2=10x$ A) $\frac{5}{y}$. B) $\frac{10}{y}$. C) $\frac{y^2}{10}$. D) $\frac{y^2}{5}$. Show Answer Correct Answer: A) $\frac{5}{y}$. 8. Find the point(s) of inflection for f(x) = 2(x)$^{1/5}$ + 3 A) None. B) X = 0. C) X = 0, 2. D) X =-2, 0, 2. Show Answer Correct Answer: B) X = 0. 9. What is the slope of the line tangent to the graph of y=ln(2x) at the point where x=4? A) 4. B) 1/4. C) 1/8. D) 1/2. E) 3/4. Show Answer Correct Answer: B) 1/4. 10. If you are looking at a sign chart, how do you find an inflection point? A) See where it goes from-to +. B) See where it goes from + to-. C) See where it goes from + to +. D) Give up. Show Answer Correct Answer: C) See where it goes from + to +. 11. Find the smallest perimeter for a rectangle with an area of 256 in$^{2}$. A) 128. B) 32. C) 64. D) 16. Show Answer Correct Answer: C) 64. 12. What is a horizontal tangent? A) Has a slope of zero. B) Has a positive slope. C) Has an undefined slope. D) Has a negative slope. Show Answer Correct Answer: A) Has a slope of zero. 13. How many points of inflection does the function $y=\frac{x+1}{x}$ A) 3. B) 1. C) 2. D) 0. Show Answer Correct Answer: D) 0. 14. $\lim_{h\rightarrow0}\left(\frac{5\left(x+h\right)^2-5x^2}{h}\right)$ A) $10x$. B) 10. C) DNE. D) $5x^2$. Show Answer Correct Answer: A) $10x$. 15. The line $y=mx+1$ $y^2=4x$ A) 1/2. B) 1. C) 3. D) 2. Show Answer Correct Answer: B) 1. 16. How many points of inflection does a parabola have? A) $1$. B) $2$. C) $0$. D) Depends on the parabola. Show Answer Correct Answer: C) $0$. 17. The Mean Value Theorem applies to f(x) = 3x-x$^{2}$ on the interval [2, 5]. Find the value of x where the slope of the tangent line is equal to the slope of the secant line A) -2. B) 2. C) -4. D) 3.5. Show Answer Correct Answer: D) 3.5. 18. What is marginal cost? A) Total cost divided by quantity. B) Fixed cost per unit. C) Rate of change of total cost with respect to quantity produced. D) Total profit at output x. Show Answer Correct Answer: C) Rate of change of total cost with respect to quantity produced. 19. If the position of a particle is represented by s(t) =-t$^{2}$ + 1, what is its position at t = 1? A) Position =-1. B) Position = 2. C) Position = 0. D) Position = 1. Show Answer Correct Answer: C) Position = 0. 20. Find the slope of the normal line at x = 9 of $f\left(x\right)=\sqrt{x}$ A) $-6$. B) $6$. C) $-\frac{1}{6}$. D) $\frac{1}{6}$. Show Answer Correct Answer: A) $-6$. 21. Find the critical points of f(x) = 2x$^{4}$-4x$^{2}$ + 1 A) X= 0. B) No critical points. C) X =-1, 0, 1. D) X =-1, 1. Show Answer Correct Answer: C) X =-1, 0, 1. 22. The value of c guaranteed to exist by the MVT for $f\left(x\right)=x^2$ A) 3/2. B) 1/2. C) 1. D) 2. Show Answer Correct Answer: A) 3/2. 23. A railroad track and a road cross at right angles. An observer stands on the road 70 meters south of the crossing and watches an eastbound train traveling at 60 meters per second. At how many meters per second is the train moving away from the observer 4 seconds after it passes through the intersection? A) 59.20. B) 57.60. C) 67.40. D) 57.88. Show Answer Correct Answer: B) 57.60. 24. If h = f(a) gives height h (in inches) of a child aged a years, then dh/da is positive when 0 < a < 10. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 25. The linearization of function y=f(x) near the value x=a is given by: A) L(a) = f(x) + f'(x) (x-a). B) L(x) = f(a) + f'(a) (x-a). C) L(a) = f'(x) + f(x) (x-a). D) L(x) = f'(a) + f(a) (x-a). Show Answer Correct Answer: B) L(x) = f(a) + f'(a) (x-a). 26. When does Newton's method fail to find an approximate zero of a function? A) Vertical tangent or distant initial guess. B) Horizontal tangent or close initial guess. C) Linear function or close initial guess. D) Exponential growth or distant initial guess. Show Answer Correct Answer: A) Vertical tangent or distant initial guess. 27. If a function has a derivative that is positive, what does that tell you? A) The function is increasing. B) The function is decreasing. C) All the above. D) None of the above. Show Answer Correct Answer: A) The function is increasing. 28. Given that $f\left(x\right)=2x^4-3x^3+4x^2$ $f^{" '}\left(x\right)$ A) $8x^3-9x^2+8x$. B) $48x-18$. C) $24x^2-18x+8$. D) $48$. Show Answer Correct Answer: B) $48x-18$. 29. If a function has a second derivative that is negative, what does that tell you? A) The function is concave up. B) The function is concave down. C) The function is decreasing. D) The function is increasing. Show Answer Correct Answer: B) The function is concave down. 30. Find the derivative of the given equationf(x) = 1/x$^{2 }$(hint:use your pink sheet) A) 2x. B) -2x$^{-3}$. C) -2x. D) 1/2x. Show Answer Correct Answer: B) -2x$^{-3}$. 31. The tangent line to f(x)$^{}$=x$^{3}$+kx$^{2}$ at x = 1 is parallel to the line containing points (2, 9) and (3, 10). What is the value of k? A) 1. B) -1. C) -2. D) 2. Show Answer Correct Answer: B) -1. 32. To be called a point of inflection of a function, what must what happen? A) First derivative must equal zero or be undefined. B) Concavity must change. C) Function must be decreasing. D) Function must be increasing. Show Answer Correct Answer: B) Concavity must change. 33. Let f(x) = x$^{3 }$and L(x) be the linearization of f(x) centered at x = 2. Find L(x). A) L(x) = 8-12(x-2). B) L(x) = 12x-8. C) L(x) = 12x-16. D) L(x) = 12x + 32. Show Answer Correct Answer: C) L(x) = 12x-16. 34. If MR(x) > MC(x) at output x, the profit-maximizing rule suggests: A) Produce more (increase output). B) Stop production immediately. C) Marginal profit is zero. D) Produce less (reduce output). Show Answer Correct Answer: A) Produce more (increase output). 35. A man 6 ft tall walks away from a lamp post 16 ft high at the rate of 5 miles per hour. How fast does the shadow lengthen? A) 5 mi/hr. B) 6 mi/hr. C) 3 mi/hr. D) 4 mi/hr. Show Answer Correct Answer: C) 3 mi/hr. 36. The minimum value of $\frac{x}{\log_ex}$ A) E. B) 1/e. C) 1. D) None of these. Show Answer Correct Answer: A) E. 37. The velocity of an object is given as v = 2t + 3t$^{3}$. What is the acceleration of the object at t = 2 secs? A) 49 m/s/s. B) 27 m/s/s. C) 38 m/s/s. D) 16 m/s/s. Show Answer Correct Answer: C) 38 m/s/s. 38. What is the "top of a hill" on a function (even if it is a cusp) called? A) Absolute maximum. B) Absolute minimum. C) Relative maximum. D) Relative minimum. Show Answer Correct Answer: C) Relative maximum. 39. When f'(x) changes from positive to negative, there is ..... A) A point of inflection. B) No maximum or minimum. C) A local maximum. D) A local minimum. Show Answer Correct Answer: C) A local maximum. 40. Evaluate:$\int_1^2x^{-3}dx$ A) $-\frac{7}{8}$. B) $\frac{15}{16}$. C) $\frac{15}{64}$. D) $-\frac{3}{4}$. E) $\frac{3}{8}$. Show Answer Correct Answer: E) $\frac{3}{8}$. 41. Suppose that the sides of a square increase from 3 cm to 3.3 cm. Estimate the change in the area of the square. A) 0.9 cm$^{2}$. B) 1.8 cm$^{2}$. C) 19.8 cm$^{2}$. D) 1.89 cm$^{2}$. Show Answer Correct Answer: B) 1.8 cm$^{2}$. 42. If $x^y=e^{\left(x-y\right)}$ $\frac{dy}{dx}$ A) Not defined. B) $\frac{\left(1+x\right)}{1+\log x}$. C) $\frac{\left(1-\log x\right)}{1+\log x}$. D) $\frac{\left(\log x\right)}{\left(1+\log x\right)^2}$. Show Answer Correct Answer: D) $\frac{\left(\log x\right)}{\left(1+\log x\right)^2}$. 43. Find the differential dy of the function y = 4x$^{2}$+x+3 A) (8x$^{2 }$+ x + 3)dx. B) (4x + 1)dx. C) (8x + 1)dx. D) None of the above. Show Answer Correct Answer: C) (8x + 1)dx. 44. A 5 ft ladder is leaning against a wall and sliding towards the floor. The top of the ladder is sliding down the wall at a rate of 2 ft/sec. How fast is the base of the ladder sliding away from the wall when the base of the ladder is 3 ft from the wall? A) 8/7 ft/sec. B) 8/3 ft/sec. C) 1 ft/sec. D) 4/3 ft/sec. Show Answer Correct Answer: B) 8/3 ft/sec. 45. A function is decreasing if its first derivative is what? A) Positive. B) Undefined. C) Zero. D) Negative. Show Answer Correct Answer: D) Negative. 46. If the position function for a particle is s(t) =-t$^{2}$-t, what is the instantaneous velocity function for the particle? A) V(t) = t$^{3}$. B) V(t) =-t. C) V(t) =-2. D) V(t)-2t-1. Show Answer Correct Answer: D) V(t)-2t-1. 47. What will be true at an inflection point? (select the best answer) A) F" (x)=0. B) F'(x)=0. C) F(x)=0. D) The function is undefined. Show Answer Correct Answer: A) F" (x)=0. 48. The absolute minimum value of x$^{4}$-x$^{2}$-2x+ 5 A) Is equal to 7. B) Is equal to 5. C) Does not exist. D) Is equal to 3. Show Answer Correct Answer: D) Is equal to 3. 49. Find dy for 2xy$^{2}$$^{ }$-x$^{2}$ +$^{ }$y = 5 if x = 0 and dx = 0.01. A) -5. B) -50. C) -0.5. D) (2x-2y$^{2}$) / (4xy + 1) dx. Show Answer Correct Answer: C) -0.5. 50. Find $\lim_{x\rightarrow0}\frac{\sqrt{1+x}-1}{\text{x}}$ A) 0. B) $\frac{1}{2}$. C) $\frac{1}{4}$. D) DNE. Show Answer Correct Answer: B) $\frac{1}{2}$. 51. Find the derivative of the function:$f\left(x\right)=e^x\sin x$ A) $e^x\cos x$. B) $-e^x\cos x$. C) $e^x\left(\cos x+\sin x\right)$. D) $e^x\left(\cos x-\sin x\right)$. Show Answer Correct Answer: C) $e^x\left(\cos x+\sin x\right)$. 52. What is the equation of the line tangent to f(x)= 4x$^{2}$+2x-1 at x=0? A) Y=2x+2. B) Y=2x-1. C) Y+1=2(x+1). D) Y=-x-1. Show Answer Correct Answer: B) Y=2x-1. 53. If the cost C (in dollars) of feeding x students in the dining center is given by C = f(x), then the units of dC/dx are dollars per student. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 54. If f'(x) >0, then the function is A) Increasing. B) Decreasing. C) Concave down. D) Concave up. Show Answer Correct Answer: A) Increasing. 55. If a function has a second derivative that is positive, what does that tell you? A) The function is increasing. B) The function is concave up. C) The function is decreasing. D) The function is concave down. Show Answer Correct Answer: D) The function is concave down. 56. The position of an object is given as a function of time by x = 3t$^{2}$ + 5t$^{3 }$-2tWhat is the acceleration of the object at time t = 2 s? A) 70 m/s/s. B) 60 m/s/s. C) 66 m/s/s. D) 64 m/s/s. Show Answer Correct Answer: C) 66 m/s/s. 57. If the line y = x touches the curve y = x$^{2}$ + bx + c at a point (1, 1) then A) B =-2, c = 1. B) B =-1, c = 1. C) B = 1, c = 2. D) B = 2, c = 1. Show Answer Correct Answer: B) B =-1, c = 1. 58. Let f(x) = x$^{3 }$and L(x) be the linearization of f(x) centered at x = 2. Calculate the approximation for f(2.1). A) 9. B) 9.261. C) 9.3. D) 9.2. Show Answer Correct Answer: D) 9.2. 59. What is the equation of the line normal to f(x)=5x$^{5}$-2x at x =-1? A) Y-3 =-1/23 (x-1). B) Y+3 =23(x+1). C) 23y =-x-1. D) Y+3 =-1/23 (x+1). Show Answer Correct Answer: D) Y+3 =-1/23 (x+1). 60. Let f(x) = $x^{(2/5)}$ A) 4.1. B) 4.0. C) 3.9. D) 3.8. Show Answer Correct Answer: C) 3.9. ← PreviousNext →Related QuizzesScience QuizzesClass 12 QuizzesClass 12 Mathematics Chapter 6 Applications Of Derivatives Quiz 1Class 12 Mathematics Chapter 6 Applications Of Derivatives Quiz 3Class 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