MCQ - Worksheet 1

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Chapter 5 Class 12 - Continuity & Differentiability - MCQ Worksheet 1 by teachoo Chapter: Chapter 5 Class 12 - Continuity & Differentiability Name: _____________________________ School: _____________________________ Roll Number: _____________________________ 1. The temperature of a cup of coffee, T(t), over time t is modeled by a function. Which of the following statements best describes why T(t) must be a continuous function? a) The temperature can be measured at any instant in time. b) The coffee cools down, so the function is always decreasing. c) The temperature cannot jump from one value to another instantaneously. d) The rate of cooling eventually slows down. 2. A company's profit P(x) from selling x units is given by a differentiable function. What does the derivative P^' (x) represent in a business context? a) The total profit from selling x units. b) The price of a single unit. c) The approximate additional profit from selling one more unit. d) The number of units needed to break even. 3. Consider the function f(x)=|x-2|. At the point x=2, the graph has a sharp corner. This corresponds to the fact that the function is: a) Continuous but not differentiable at x=2. b) Differentiable but not continuous at x=2. c) Neither continuous nor differentiable at x=2. d) Both continuous and differentiable at x=2. 4. The amount of water W(t) in a reservoir over a year is modeled by a continuous function. If W( January )=500 megaliters and W( March )=400 megaliters, what theorem guarantees that there was a time t between January and March when the water level was exactly 450 megaliters? a) Rolle's Theorem b) Mean Value Theorem c) Intermediate Value Theorem d) Squeeze Theorem 5. The function f(x)=[x] (the greatest integer function) is often used to model scenarios where values are truncated or rounded down. The discontinuity at integer values implies: a) The scenario is impossible to model. b) An abrupt change occurs whenever a whole number is reached. c) The function grows infinitely large. d) The function is not defined at integers. 6. If a function f is differentiable at a point c, what must be true? a) The function must be a polynomial. b) The function must also be continuous at c. c) The derivative of the function must be zero at c. d) The function must be increasing at c. 7. The chain rule is most analogous to which of the following real-world scenarios? a) The total cost of items in a shopping cart. b) The speed of a car relative to the ground, when you know its speed relative to a moving train. c) The changing rate of a person's height over their lifetime. d) The effect of gravity on a falling object. 8. The function f(x)={■(2x&" if " x≤1@3x-1&" if " x>1)┤ models a tax system. The function is continuous at x=1. What does this imply for someone whose income is exactly 1 unit? a) They pay no tax. b) There is no sudden jump in the tax owed as their income crosses the 1 unit threshold. c) The tax rate is the same for everyone. d) The tax system is unfair. 9. The derivative of an even function is: a) Always an even function. b) Always an odd function. c) Could be even or odd. d) Always a constant function. 10. A function f(x) represents the altitude of a hiker on a trail, where x is the distance from the start. If f^' (x)=0 for a certain stretch of the trail, it means: a) The hiker is at the starting point. b) The hiker is at the highest point of the trail. c) The trail is flat for that stretch. d) The hiker has stopped walking. Important links Answer of this worksheet - https://www.teachoo.com/25572/5352/MCQ---Worksheet-1/category/Teachoo-Questions---MCQs/ Full Chapter with Explanation, Activity, Worksheets and more – https://www.teachoo.com/subjects/cbse-maths/class-12th/ 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 temperature cannot jump from one value to another instantaneously. c) The approximate additional profit from selling one more unit. a) Continuous but not differentiable at x=2. c) Intermediate Value Theorem. b) An abrupt change occurs whenever a whole number is reached. b) The function must also be continuous at c. b) The speed of a car relative to the ground, when you know its speed relative to a moving train. b) There is no sudden jump in the tax owed as their income crosses the 1 unit threshold. b) Always an odd function. c) The trail is flat for that stretch.