What is the extreme (x^2-a^2)^2 ?

The extreme (x^2-a^2)^2 is {a 0: Maximum(0,a^4)}

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extreme (x^2-a^2)^2

extreme

{a < 0 or a > 0 : Maximum (0, a^{4})}

Solution steps

Find the critical points:

x = 0, x = - a, x = a

f^{''} (x) = 4 (3 x^{2} - a^{2})

Check the sign of

f^{''} (x) = 4 (3 x^{2} - a^{2})

at each critical point

Check critical point

x = 0 : {a < 0 or a > 0 : Maximum (0, a^{4})}

{a < 0 or a > 0 : Maximum (0, a^{4})}

What is the extreme (x^2-a^2)^2 ?
The extreme (x^2-a^2)^2 is {a<0\lor a>0: Maximum(0,a^4)}