What is the extreme f(x)= 1/4 x^4-4x^2+2 ?

The extreme f(x)= 1/4 x^4-4x^2+2 is Minimum(-2sqrt(2),-14),Maximum(0,2),Minimum(2sqrt(2),-14)

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extreme f(x)= 1/4 x^4-4x^2+2

extreme points

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

Minimum (- 22, - 14), Maximum (0, 2), Minimum (22, - 14)

Solution steps

f^{'} (x) = x^{3} - 8 x

Find intervals:

Decreasing

: - \infty < x < - 22,

Increasing

: - 22 < x < 0,

Decreasing

: 0 < x < 22,

Increasing

: 22 < x < \infty

Plug

x = - 22

into

\frac{1}{4} x^{4} - 4 x^{2} + 2 : - 14

Minimum (- 22, - 14)

Plug

x = 0

into

\frac{1}{4} x^{4} - 4 x^{2} + 2 : 2

Maximum (0, 2)

Plug

x = 22

into

\frac{1}{4} x^{4} - 4 x^{2} + 2 : - 14

Minimum (22, - 14)

Minimum (- 22, - 14), Maximum (0, 2), Minimum (22, - 14)

300 x - 4 x^{3}

x^{3} + 12 x^{2} - 27 x + 2

f (x) = x^{3} - 9 x^{2} + 15 x - 4

P (x, y) = 3 x^{2} y + 4 x y^{2} - y^{- 4}

f (x) = (x + 10) (\frac{60}{x} + 6)

What is the extreme f(x)= 1/4 x^4-4x^2+2 ?
The extreme f(x)= 1/4 x^4-4x^2+2 is Minimum(-2sqrt(2),-14),Maximum(0,2),Minimum(2sqrt(2),-14)