Find all intervals for which the graph of the function y=(8x^3) - (2x^4) is concave downward.
Concavity is test with the second derivative test.
What is the 2nd derivative of y?
The first is $\displaystyle y'=24x^2-8x^3$
Once you have the second derivative, set $\displaystyle y''=0$ to obtain the inflection points.
Spoiler: