Question

For what values of a does the minimum value of the function $y=x^2-4ax-a^4$ assume the greatest value?

Answer 1

$y=x^2-4ax-a^4$

$y^1=2x-4a=0$

$y^{11}=2>0$ (Minimum at $x=2a$)

$y(x=2a)={4a}^2-4a\left(2a\right)-a^4$

$=-(a^4+{4a}^2)$

for $a=0$, $y$ function will be maximum.