Unit 4 of 5
Study guide for CLEP CLEP Calculus — Unit 4: Applications. Practice questions, key concepts, and exam tips.
15
Practice Questions
17
Flashcards
5
Key Topics
Try these 5 questions from this unit. Sign up for full access to all 15.
Economics: A company's cost is C(x) = + 2x + 5. What is marginal cost when x = 3?
4
6
8
10
12
Answer: C — 8 is correct because marginal cost is derivative of cost, C'(x) = 2x + 2, so C'(3) = 8.
A function f(x) is approximated by its linearization at x = 2, where f(2) = 3 and f'(2) = 4. Which of the following is a correct statement about the approximation?
The approximation is an overestimate of f(x) when x > 2 and an underestimate when x < 2.
The approximation is an overestimate of f(x) for all x except x = 2.
The approximation is always an overestimate of f(x) for all x.
The approximation is always an underestimate of f(x) for all x.
The approximation is an underestimate of f(x) when x > 2 and an overestimate when x < 2.
Answer: E — Since f'(2) is positive, the linearization has a positive slope, meaning it underestimates f(x) for x > 2 and overestimates for x < 2.
A company has a cost function C(x) = + 5x + 100. What is the cost when x = 10?
250
300
350
400
450
Answer: C — 350 is correct because C(10) = 2(10)^2 + 5(10) + 100 = 200 + 50 + 100 = 350.
A particle moves in the plane according to the parametric equations x(t) = and y(t) = 2t. What does the definite integral of the velocity vector represent?
The particle's total distance traveled over the interval of time
The particle's displacement over the interval of time
The particle's speed over the interval of time
The particle's acceleration over the interval of time
The particle's average velocity over the interval of time
Answer: B — The definite integral of the velocity vector represents the particle's displacement, or net change in position, over the interval of time.
The half-life of a certain radioactive substance is 10 years. If we start with 100 grams of this substance, how much will be left after 20 years?
60 grams
30 grams
40 grams
50 grams
25 grams
Answer: E — The correct option is "25 grams" because after one half-life, 50 grams remain, and after another half-life, half of 50 grams, which is 25 grams, remains, illustrating the concept of exponential decay. This process occurs due to the substance's radioactive nature, where the amount of substance decreases by half every 10 years.
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