### Home > CALC > Chapter 7 > Lesson 7.2.2 > Problem7-78

7-78.

$F ( x ) = \int _ { 0 } ^ { x } f ( t ) d t$ for the function $f(t)$ graphed at right.

1. When is $F(x)$ at a maximum on $[0, 15]$?

An integral represents the area under a curve. At which point is there the largest area?

2. Is $F(x)$ increasing or decreasing or both on $[0, 8]$?

Strictly Increasing. (Justify.)

3. Find $F(4)$, $F(10)$, and $F(15)$.

$F(10)=\int_{0}^{10}f(t)dt=$ quarter circle $+$ triangle $+$ trapezoid

4. List the interval(s) on $[0, 15]$ for which $F^{\prime\prime}(x) > 0$.

Since $F^\prime(x) = f(x)$$F^{\prime\prime}(x) = f^\prime(x)$.