AP Calculus BC Unit 4 practice questions: Contextual Applications of Differentiation
8 original multiple-choice questions on AP Calc BC Unit 4, contextual applications of differentiation. Answer each one in your browser and read the explanation, then review the key ideas below.
Question 1 of 8
Use L'Hospital's rule to evaluate lim (x→0) of (1 − cos x)/x².
Question 2 of 8
The radius of a circle grows at 2 cm/s. How fast is the area growing when the radius is 5 cm?
Question 3 of 8
Use the tangent line to f(x) = √x at x = 4 to estimate √4.1.
Question 4 of 8
A particle's position is s(t) = t³ − 6t². What is its velocity at t = 2?
Question 5 of 8
A particle has velocity v(t) = t² − 4 for t ≥ 0. When is it at rest?
Question 6 of 8
Evaluate lim (x→∞) of x/eˣ.
Question 7 of 8
A 10-ft ladder leans against a wall. Its base slides away at 2 ft/s. How fast is the top sliding down when the base is 6 ft from the wall?
Question 8 of 8
A particle has velocity v(t) = 3t². What is its acceleration at t = 2?
Key ideas in Unit 4
- For motion, velocity is the derivative of position and acceleration is the derivative of velocity. A particle is at rest when v = 0 and speeds up when v and a have the same sign.
- Related rates: write an equation linking the quantities, differentiate with respect to time, then substitute the known values last.
- Local linearization: near x = a, f(x) ≈ f(a) + f′(a)(x − a). It overestimates when f is concave down and underestimates when concave up.
- L'Hospital's rule applies only to 0/0 or ∞/∞ forms: take the limit of f′/g′.
More AP Calc BC practice
← Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
Unit 5: Analytical Applications of Differentiation →
The full AP Calculus BC practice test, all units
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