The x coordinates of the points of inflection of the graph of $\displaystyle y= x^5-5x^4=3x+7$ are...

A 0,

B 1,

C 3,

D 0 and 3,

E 0 and 1

$\displaystyle y''=20x^3-60x^2$

Simplify.

$\displaystyle y''=20x^2(x-3)$

So, thanks to the graph and knowledge of the definition of inflection point (y''= 0).

I choose D.

However, the book says C.

I'm inclined to believe it is right because I did the sign test for 0 for numbers less than 0 and less than 3, thought I may be incorrect of which function to put the test values into (y'' right?), and got the same sign (negative).

So, did I do the sign test wrong? Or is the right and I'm confusing myself with these questions.

What is the answer to the problem?

Thank you.