Mathematics

Mathematics

Problem

Let

f

be continuous on

0 \le x \le 8

with

f(x) > 0

for

0 < x < 4

and

f(x) < 0

for

4 < x < 8

. Define the accumulation function

F(x)=\displaystyle\int_{0}^{x} f(t)\,dt

for

0 \le x \le 8

. Which of the following best describes the monotonic behavior of

F

on

(0,8)

? a)

F

is decreasing on

(0,4)

and increasing on

(4,8)

. b)

F

is increasing on

(0,8)

. c)

F

is increasing on

(0,4)

and decreasing on

(4,8)

. d)

F

is increasing on

(0,4)

and constant on

(4,8)

.

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