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

The extreme f(x)=x^4-5x^2+4 is Minimum(-sqrt(5/2),-9/4),Maximum(0,4),Minimum(sqrt(5/2),-9/4)

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

extreme points

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

Minimum (- \frac{5}{2}, - \frac{9}{4}), Maximum (0, 4), Minimum (\frac{5}{2}, - \frac{9}{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} + 4 : - \frac{9}{4}

Minimum (- \frac{5}{2}, - \frac{9}{4})

Plug

x = 0

into

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

Maximum (0, 4)

Plug

x = \frac{5}{2}

into

x^{4} - 5 x^{2} + 4 : - \frac{9}{4}

Minimum (\frac{5}{2}, - \frac{9}{4})

Minimum (- \frac{5}{2}, - \frac{9}{4}), Maximum (0, 4), Minimum (\frac{5}{2}, - \frac{9}{4})

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

f (x) = x^{2} - 4 x - 1

f (x, y) = \frac{1}{x ^{2} + y ^{2} - 1}

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

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

What is the extreme f(x)=x^4-5x^2+4 ?
The extreme f(x)=x^4-5x^2+4 is Minimum(-sqrt(5/2),-9/4),Maximum(0,4),Minimum(sqrt(5/2),-9/4)