### Home > APCALC > Chapter 8 > Lesson 8.3.1 > Problem8-105

8-105.

Multiple Choice: If $F ( x ) = \int _ { 0 } ^ { x } \sqrt { 9 - t } d t$, which of the following statements are true? Homework Help ✎

1. $F^\prime(5) = 2$

1. $F(−7) > F(5)$

1. $F$ is concave downward

 A. I only B. II only C. I and III D. II and III E. I and II

Recall that the derivative of an integral gives you the original function (FTC, part 1).

$\text{Visualize the graph of }y=\sqrt{9-x}.$

$\text{Without computing, compare }F(-7)=\int_{0}^{-7}\sqrt{9-x}dx\text{ with }F(5)=\int_{0}^{5}\sqrt{9-x} dx.$

Which is greater?

The derivative of the integral, F(x), gives you the original function, f(x).
So, the derivative of the original function will give you the second derivative of F(x).