MCQ - Worksheet 1

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Chapter 6 Class 12 - Application of Derivatives - MCQ Worksheet 1 by teachoo Chapter: Chapter 6 Class 12 - Application of Derivatives Name: _____________________________ School: _____________________________ Roll Number: _____________________________ 1. The radius of a spherical balloon is increasing. The rate of change of its volume is fastest when: a) The radius is smallest. b) The rate of change of the radius is slowest. c) The radius is largest. d) The balloon is fully inflated. 2. A company's marginal cost is the derivative of its cost function, C^' (x). If C^' (100)=15, what does this signify? a) The total cost of producing 100 items is $15. b) The average cost per item is $15. c) The cost to produce the 101st item is approximately $15. d) The company makes a profit of $15 on the 100th item. 3. A function f(x) represents the temperature of a chemical reaction over time. If f^' (t)>θ and f^' (t)<0 for a specific time interval, it means: a) The temperature is rising at an increasing rate. b) The temperature is falling at a decreasing rate. c) The temperature is rising, but the rate of increase is slowing down. d) The temperature is falling at an increasing rate. 4. To find the dimensions of a rectangle with a fixed perimeter that has the maximum possible area, one should look for a point where: a) The second derivative of the area function is positive. b) The first derivative of the area function is zero and the second derivative is negative. c) The first derivative of the area function is positive. d) The area function itself is equal to zero. 5. The function f(x)=x^∧ 3 has f^' (0)=0. What is true about the point x=0 ? a) It is a local maximum. b) It is a local minimum. c) It is a point of inflection. d) It is a point of discontinuity. 6. A ladder is leaning against a wall and its base is being pulled away from the wall. The rate at which the top of the ladder slides down the wall is: a) Constant. b) Faster when the ladder is more vertical. c) Slower when the ladder is more vertical. d) Equal to the rate at which the base is pulled. 7. For a function f(x) on a closed interval [a,b], the absolute maximum value can occur: a) Only where f^' (x)=0. b) Only at the endpoints a or b. c) Either at a point where f^' (x)=0 or at an endpoint. d) Only where the function is increasing. 8. If f^' (x) changes sign from negative to positive as x increases through a point c, then c is a: a) Point of inflection. b) Local maximum. c) Y-intercept. d) Local minimum. 9. The profit function for a product is P(x). To maximize profit, the company should produce a quantity x where: a) The marginal revenue equals the marginal cost. b) The total revenue is highest. c) The cost per item is lowest. d) The profit function is positive. 10. The height of a projectile is given by h(t)=-16t^2 +v_0 t+h_0. The maximum height is reached when: a) The projectile hits the ground (h(t)=0). b) The time t is zero. c) The velocity h^' (t) is zero. d) The acceleration h^'' (t) is zero. Important links Answer of this worksheet - https://www.teachoo.com/25580/5356/MCQ---Worksheet-1/category/Teachoo-Questions---MCQs/ Full Chapter with Explanation, Activity, Worksheets and more – https://www.teachoo.com/subjects/cbse-maths/class-12th/ch6-12th-application-of-derivatives/ Maths Class 12 - https://www.teachoo.com/subjects/cbse-maths/class-12th/ For more worksheets, ad-free videos and Sample Papers – subscribe to Teachoo Black here - https://www.teachoo.com/black/   Answer Key to MCQ Worksheet 1 c) The radius is largest. (Since dV/dt=4πr^2 (dr/dt), the rate is proportional to r^2 ). c) The cost to produce the 101st item is approximately $15. c) The temperature is rising, but the rate of increase is slowing down. ( f^'>0 means rising, means concave down, so the slope is decreasing). b) The first derivative of the area function is zero and the second derivative is negative. c) It is a point of inflection. (The derivative is positive on both sides of 0 ). c) Slower when the ladder is more vertical. (The rate of vertical change is inversely related to the horizontal distance from the wall). c) Either at a point where f^' (x)=0 or at an endpoint. d) Local minimum. a) The marginal revenue equals the marginal cost. (This is where the derivative of the profit function, P^' (x)=R^' (x) C^' (x), is zero). c) The velocity h^' (t) is zero.