Show that if $f'(a)=0$ and $f^{(4)}(a)>0$, then $a$ is a minima of $f$

Question

I need to show that if $f'(a)=0$ and $f^{(4)}(a)>0$, then $a$ is a minima of $f$

I could show, without difficulty, that if $f'(a)=0$ and $f''(a)>0$, then $a$ is a minima of $f$.

Can I show that if $f^{(4)}(a)>0$ then $f''(a)>0$? If I do that, I can use what a I already know.

Answer 1

False. $$ x^4 - x^2 $$ at the origin. Note $x^4 - x^2 = x^2 (x^2 - 1)$ and is negative near the origin.