This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 6 Applications Of Derivatives – Quiz 4 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 6 Applications Of Derivatives Quiz 4 (21 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. What is the equation of the line tangent to y= x$^{2}$+2x-1 at x=1? A) Y=2x-2. B) Y=2x. C) Y=4x. D) Y=4x-2. Show Answer Correct Answer: D) Y=4x-2. 2. F has critical numbers of-3, 0, and 1. If $f" (x) =-3x^2 + 4x$ A) -3. B) 0. C) 1. D) None. Show Answer Correct Answer: C) 1. 3. Given:MR(x)=100-5x, MC(x)=20 + 2x. Solve MR = MC to find profit-maximizing output. A) X = 12. B) X = 5. C) X = 10. D) X = 8. Show Answer Correct Answer: A) X = 12. 4. When a car's velocity is positive and its acceleration is positive, what is happening to the car's motion? A) The car remains at rest. B) The car travels at a constant speed. C) The car speeds up. D) The car slows down. Show Answer Correct Answer: C) The car speeds up. 5. If f'(x) = 0 what does that imply about the x value? A) It is a relative maximum. B) It is an inflection value. C) F(x) does not exist at that value. D) It is a critical point. Show Answer Correct Answer: D) It is a critical point. 6. When f'(x) changes from positive to negative, there is(are) ..... A) A maximum. B) A minimum. C) No extrema. D) None of the above. Show Answer Correct Answer: A) A maximum. 7. The derivative of the function g is $g'\left(x\right)=\cos\left(\sin x\right).$ $x=0$ A) I only. B) II only. C) I and III only. D) I, II, III. Show Answer Correct Answer: A) I only. 8. A particle moves in a straight line with a velocity of v(t) = 2t$^{2}$. How far does the particle move between times t = 1 and t = 3? A) 26/3. B) 18. C) 52/3. D) 16. Show Answer Correct Answer: C) 52/3. 9. For a function g(x), g'(-2)=0 indicates that x=-2 is ..... A) A relative minimum. B) An inflection point. C) A relative maximum. D) A critical point. Show Answer Correct Answer: D) A critical point. 10. Identify the conclusion of the Mean Value Theorem. A) $f'\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$. B) $f'\left(c\right)=0$. C) All the above. D) None of the above. Show Answer Correct Answer: A) $f'\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}$. 11. S(t) = t$^{2}$-20 Find the average velocity from t = 3 to t = 5. A) 4. B) 2. C) 8. D) 6. Show Answer Correct Answer: C) 8. 12. The line y = mx + 1 is a tangent to the curve y$^{2}$ = 4x, if the value of m is A) 2. B) $\frac{1}{2}$. C) 3. D) 1. Show Answer Correct Answer: D) 1. 13. Nature of the function f(x) = e$^{2x}$ is ..... A) Increasing. B) Decreasing. C) Constant. D) Increasing and decreasing. Show Answer Correct Answer: A) Increasing. 14. $\lim_{x\rightarrow2}\left(\frac{x^2-4}{x-2}\right)$ A) 8. B) 2. C) 6. D) 4. Show Answer Correct Answer: D) 4. 15. Identify the critical points of the following function:$^{}$g(x)=2x$^{3}$-3x$^{2}$ A) X=0, 1. B) X=-1, 1. C) X=0, -1. D) X=0, 0. Show Answer Correct Answer: A) X=0, 1. 16. In a cone, find the rate of change of the volume if dr/dt is 2 inches per minute and the height is 3r when the radius is 6. A) 216pi cubic in/min. B) 128pi cubic in/min. C) -128pi cubic in/min. D) -216pi cubic in/min. Show Answer Correct Answer: A) 216pi cubic in/min. 17. TRUE OR FALSE? If f is continuous on [-1, 1], f(-1)=4 and f(1)=-2, then there is a zero between-1 and 1. A) TRUE. B) FALSE. C) CANNOT BE DETERMINED. D) None of the above. Show Answer Correct Answer: A) TRUE. 18. Which of the following theorems may be applied to the function $y=\left|x-3\right|+b, \\b>0, $ A) I only. B) II only. C) III only. D) II and III only. E) I, II, and III. Show Answer Correct Answer: D) II and III only. 19. A rectangular solid that has a square base has a surface area of 150 square inches. Find the maximum volume of the solid. (use Calculus) A) 5. B) 150. C) 125. D) 250. Show Answer Correct Answer: C) 125. 20. Given the function $u(x) = \ln(x)-x + 2$ $x = 1$ A) Relative Minimum. B) Neither. C) Cannot be determined. D) Relative Maximum. Show Answer Correct Answer: D) Relative Maximum. 21. Rachel is standing atop a 13ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3ft/sec. How fast is the angle changing between the base of the ladder and the ground when the ladder is 5 ft high? A) .65 deg/sec. B) -1.44 deg/sec. C) .5 deg/sec. D) 1.5 deg/sec. Show Answer Correct Answer: B) -1.44 deg/sec. ← PreviousRelated 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 3Class 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