### Home > CALC > Chapter 5 > Lesson 5.1.1 > Problem 5-7

5-7.

You know that the first derivative, , tells us the slope and the rate of change of

*.*

What does the

*second derivative*,, tell you about? What doestell you about?tells us the same thing aboutthattells us about.Find

andfor.::Use these derivatives to find

and. Isgetting steeper or less steep at? At? Explain your reasoning.Consider this: Even though a slope of

is steeper than a slope of , if the slope changes from to , then the slope is decreasing. The values in part (c) can be used to determine concavity. Where is

concave up? Where isconcave down?Positive values of the 2nd-derivative indicate that the function is concave up while negative values indicate that the function is concave down.