Chapter 4, Problem 7PS

Extrema and Points of Inflection The graph of the function f consists of the three line segments joining the points (0, 0), $(2,-2)$, (6, 2), and (8, 3). The function F is defined by the integral

$F(x)={\displaystyle {\int }_0^{x}f(t)dt}$

(a) Sketch the graph of f.

(b) Complete the table.

x	0	1	2	3	4	5	6	7	8
F(x)

(c) Find the extrema of F on the interval [0, 8].

(d) Determine all points of inflection of F on the interval (0, 8).