What is the extreme f(x)=x^4-5x^2 ?

The extreme f(x)=x^4-5x^2 is Minimum(-sqrt(5/2),-25/4),Maximum(0,0),Minimum(sqrt(5/2),-25/4)

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extreme f(x)=x^4-5x^2

extreme points

f (x) = x^{4} - 5 x^{2}

Minimum (- \frac{5}{2}, - \frac{25}{4}), Maximum (0, 0), Minimum (\frac{5}{2}, - \frac{25}{4})

Solution steps

f^{'} (x) = 4 x^{3} - 10 x

Find intervals:

Decreasing

: - \infty < x < - \frac{5}{2},

Increasing

: - \frac{5}{2} < x < 0,

Decreasing

: 0 < x < \frac{5}{2},

Increasing

: \frac{5}{2} < x < \infty

Plug

x = - \frac{5}{2}

into

x^{4} - 5 x^{2} : - \frac{25}{4}

Minimum (- \frac{5}{2}, - \frac{25}{4})

Plug

x = 0

into

x^{4} - 5 x^{2} : 0

Maximum (0, 0)

Plug

x = \frac{5}{2}

into

x^{4} - 5 x^{2} : - \frac{25}{4}

Minimum (\frac{5}{2}, - \frac{25}{4})

Minimum (- \frac{5}{2}, - \frac{25}{4}), Maximum (0, 0), Minimum (\frac{5}{2}, - \frac{25}{4})

What is the extreme f(x)=x^4-5x^2 ?
The extreme f(x)=x^4-5x^2 is Minimum(-sqrt(5/2),-25/4),Maximum(0,0),Minimum(sqrt(5/2),-25/4)