Defining Functions Using the Fundamental Theorem

A function defined by an integral The graph of a function ƒ consists of a semicircle and two line segments as shown. Let

a. Find g(1).

b. Find g(3).

c. Find g(-1)

d. Find all values of x on the open interval ( -3, 4) at which g has a relative maximum.

e. Write an equation for the line tangent to the graph of g at x = -1.

f. Find the x-coordinate of each point of inflection of the graph of g on the open interval ( -3, 4)

g. Find the range of g.

Step 1 :

In this problem, we have to find g(1), g(3), g(-1) and find the equation of tangent line then find the range of g(x).