CPM Homework Help : CALC Problem 8-104

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

$F^\prime(5) = 2$

$F(−7) > F(5)$

$F$ is concave downward

I only

II only

I and III

II and III

I and II

Hint 1:

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

Hint 2:

Which is greater?

Hint 3:

III. 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 2nd-derivative of $F(x)$ .