AP Calculus Slides December 10, 2007

Applications of Derivatives ... Pre-Test

Calculus Studies

The graph of the function is increasing on which of the following intervals?

(A) I only (B) II only (C) III only (D) I and II only (E) I and III only

I 1 < x II 0 < x < 1 III x < 0

Let: For how many inputs c between a = -2 and b = 2 is it true that

The table below gives some values of the derivative of a function g.

Based on this information it appears that on the interval covered by the table

(A) g is increasing and concave up everywhere

(B) g is increasing and concave down everywhere

(C) g has a point of inflection

(D) g is decreasing and concave up everywhere

(E) g is decreasing and concave down everywhere

(A) 3.80 (B) 3.84 (C) 3.88 (D) 3.92 (E) 3.96

Suppose ƒ is a continuous and differentiable function on the interval [0, 1] and g(x) = ƒ(3x). The table below gives some values of ƒ.

What is the approximate value of g'(0.1)?

If has a local minimum at x = 4 then the value of k is:

(A) -1 (B) (C) 1 (D) 4 (E) None of these

Let ƒ be a function given by

(a) Find the domain of ƒ.

(b) On the graph below, sketch the graph of ƒ.

(c) Write an equation for each horizontal asymptote of the graph of ƒ.

(d) Find the range of ƒ. [Use to justify your answer.]