Module 5 DBA - Ap Calculus AB. The following questions are NON-CALCULATOR. Show
all work.
(-6.2)
Ο
(3,2)
Graph of f'
The function f is differentiable on the closed interval [-6, 5] and satisfies f(-2) = 7. The graph of f', the
derivative of f, consists of a semicircle and three line segments, as shown in the figure above.
1). Use the above graph of f' to answer the following questions
a). On what intervals is f increasing and concave down. Justify your answers
b). Find all values of x on the interval -6 inflection. Justify your answers.
c). Find all values of x on the interval -6 minimum. Justify your answers.
d). On what intervals is f decreasing? Justify your answers.
2).
X
g(x)
1
4
-2
7
6
8
-5
4
2
252
g'(x)
h(x)
1
h'(x)
-1
6
4
8
0
10
-6
-4
1
The functions g and h are differentiable for all real numbers and h is strictly increasing.
The table above gives values of the functions and their first derivatives at selected
values of x. The function f is given by f(x) = g(h(x)) + 2
a). Explain why there must be a value c for 1 b). Explain why there must be a value r for 1 c). If h¹ is the inverse of h write an equation for the line tangent to the graph of y =
h-1(x) at x=6
d). For the given function of f(x), Find f'(1)