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 points

(x^{2} - a^{2})^{2}

{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})}

f (x, y) = y^{3} + 2 x^{2} + 3 x y - y^{2} - 3 x - y + 3

f (x) = e^{x} (x - 3)

f (x) = 4 x^{3} + 12 x^{2} - 36 x

f (x, y) = 8 x ln (x) y

f (x) = \frac{1}{4} x^{4} - 2 x^{3} + 2

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)}