Home > CALC > Chapter 5 > Lesson 5.1.1 > Problem 5-7
5-7.
You know that the first derivative,
What does the second derivative,
, tell you about ? What does tell you about ? tells us the same thing about that tells us about . Find
and for . : : Use these derivatives to find
and . Is getting 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 is concave down? Positive values of the 2nd-derivative indicate that the function is concave up while negative values indicate that the function is concave down.