Question

Let f(x) = 8 x^3 + 192 x^2 + 71 x - 43

Use the second derivative rule to determine the values of x for which the graph of f is concave up and those on which it is concave down.

Hint: Use what you know about the shape of cubic polynomial graphs from Algebra and Precalculus.

The graph of f is concave upward for the following values of x:

Answer 1

heres an example: Step 1: Take the derivative:

f'(x)=8x-20
This gives you an equation of a line. To find where the derivative is greater than zero, you want to find where this equation is positive.

To do this solve the inequality:
8x-20>0




In interval notation this is the same as:
a<x<infinity a=20/8

, where a=20/8.

Now repeat the process, but with the less than symbol instead of the greater than symbol

Answer 2

why did the instructions ask for the second derivative?