What is the extreme f(x)=x^4-128x^2+5 ?

The extreme f(x)=x^4-128x^2+5 is Minimum(-8,-4091),Maximum(0,5),Minimum(8,-4091)

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extreme f(x)=x^4-128x^2+5

extreme points

f (x) = x^{4} - 128 x^{2} + 5

Minimum (- 8, - 4091), Maximum (0, 5), Minimum (8, - 4091)

Solution steps

f^{'} (x) = 4 x^{3} - 256 x

Find intervals:

Decreasing

: - \infty < x < - 8,

Increasing

: - 8 < x < 0,

Decreasing

: 0 < x < 8,

Increasing

: 8 < x < \infty

Plug

x = - 8

into

x^{4} - 128 x^{2} + 5 : - 4091

Minimum (- 8, - 4091)

Plug

x = 0

into

x^{4} - 128 x^{2} + 5 : 5

Maximum (0, 5)

Plug

x = 8

into

x^{4} - 128 x^{2} + 5 : - 4091

Minimum (8, - 4091)

Minimum (- 8, - 4091), Maximum (0, 5), Minimum (8, - 4091)

x y - 3 x^{2} - 2 y^{2}

\frac{2 x}{x ^{2} + x - 20} \frac{3 x}{x ^{2} + 4 x - 5}

f (x) = 2 x^{3} - 12 x^{2} + 14

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

f (x) = e^{x^{3} - 27 x}

What is the extreme f(x)=x^4-128x^2+5 ?
The extreme f(x)=x^4-128x^2+5 is Minimum(-8,-4091),Maximum(0,5),Minimum(8,-4091)