AP Calculus AB Problems with Solutions (Part - 7)

Problem 1 :

If f(x) = (sin x)^-⅓, find f'(x).

Solution :

Problem 2 :

In the above limit, L is a real number. Which of the following must be true?

A)  I only

B)  I and II

C)  I and III

D)  II and III

E)  I, II and III

Solution :

Problem 3 :

Estimate f'(3) based on the information in the table below.

Solution :

Problem 4 :

For questions 1-3, consider the function f'(x) shown above with domain all real numbers.

1. Determine the interval(s) in which f(x) is concave down. Justify.

2. Identify the x-values of local extrema on f and identify the type. Justify.

3. Identify the x-values of all points of inflection on f. Justify.

Solution :

Problem 5 :

A piece of land is shaped like a right triangle. Two people start at the right angle at the same time and walk at the same speed along different legs of the triangle while spraying the land. If the area covered is changing at 4 m²/s, how fast are the people moving when they are each 3 m from the right angle?

Solution :

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