# Thread: Calculus Interval Math Problem

1. ## Calculus Interval Math Problem

Find all intervals for which the graph of the function y=(8x^3) - (2x^4) is concave downward.

2. Concavity is test with the second derivative test.

What is the 2nd derivative of y?

The first is $y'=24x^2-8x^3$

Once you have the second derivative, set $y''=0$ to obtain the inflection points.

Spoiler:
$y''=48x-24x^2=0\Rightarrow 24x(2-x)=0\Rightarrow x=0,2$

What does this tell you now?