What is the extreme f(x)=2x^4-20x^2+18 ?

The extreme f(x)=2x^4-20x^2+18 is Minimum(-sqrt(5),-32),Maximum(0,18),Minimum(sqrt(5),-32)

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extreme f(x)=2x^4-20x^2+18

extreme points

f (x) = 2 x^{4} - 20 x^{2} + 18

Minimum (- 5, - 32), Maximum (0, 18), Minimum (5, - 32)

Solution steps

f^{'} (x) = 8 x^{3} - 40 x

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < 0,

Decreasing

: 0 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = - 5

into

2 x^{4} - 20 x^{2} + 18 : - 32

Minimum (- 5, - 32)

Plug

x = 0

into

2 x^{4} - 20 x^{2} + 18 : 18

Maximum (0, 18)

Plug

x = 5

into

2 x^{4} - 20 x^{2} + 18 : - 32

Minimum (5, - 32)

Minimum (- 5, - 32), Maximum (0, 18), Minimum (5, - 32)

- x^{2} + 4 x + 6

f (x, y) = x^{2} y - 15 x y^{2} + 12 y

f (x, y) = - 2 x^{3} + 6 x y + 3 y^{3}

f (x, y) = x^{2} + 4 y^{2} - 2 x + 8 y - 1

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

What is the extreme f(x)=2x^4-20x^2+18 ?
The extreme f(x)=2x^4-20x^2+18 is Minimum(-sqrt(5),-32),Maximum(0,18),Minimum(sqrt(5),-32)