Question

The graph of y=(5x^4)-x^5 has inflection points where?

Answer 1

The answer choices are:
(A) (0,0) only
(B) (3,162) only
(C) (4,256) only
(D) (0,0) and (3,162)
(E) (0,0) and (4,256)

Answer 2

I thought it was only (3,162) because the second derivative only changes signs at x=3, but the graph shows that (0,0) is also a point of inflection.

Answer 3

\(\large f(x)=5x^4-x^5 \)
\(\large {f'(x)=20x^3-5x^4}\)
\(\large f''(x)=60x^2-20x^3\)
set the second derivative equal to zero and test points between those given x's. If there's a change in concavity then that means there's in inflection point happening in the graph.
\(\large {-20x^2(x-3)=0}\)
\(\large x=3\)
and
\(\large x=0\)