### 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?

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

1. $F(−7) > F(5)$

1. $F$ is concave downward

1. I only

1. II only

1. I and III

1. II and III

1. 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, $F\left(x\right)$, gives you the original function, $f\left(x\right)$.
So, the derivative of the original function will give you the second derivative of $F\left(x\right)$.