What is the extreme f(x)=2x^4-36x^2 ?

The extreme f(x)=2x^4-36x^2 is Minimum(-3,-162),Maximum(0,0),Minimum(3,-162)

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extreme f(x)=2x^4-36x^2

extreme points

f (x) = 2 x^{4} - 36 x^{2}

Minimum (- 3, - 162), Maximum (0, 0), Minimum (3, - 162)

Solution steps

f^{'} (x) = 8 x^{3} - 72 x

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

2 x^{4} - 36 x^{2} : - 162

Minimum (- 3, - 162)

Plug

x = 0

into

2 x^{4} - 36 x^{2} : 0

Maximum (0, 0)

Plug

x = 3

into

2 x^{4} - 36 x^{2} : - 162

Minimum (3, - 162)

Minimum (- 3, - 162), Maximum (0, 0), Minimum (3, - 162)

f (x) = 25 (x^{2} - y^{2}) - 2 (x^{2} + y^{2})^{2}

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

f (x, y) = 80 x^{\frac{4}{10}} y^{\frac{2}{10}}

5 (x - 4)^{\frac{2}{3}}

f (x) = 5 x^{2} y + 3 x y^{8} + 23

What is the extreme f(x)=2x^4-36x^2 ?
The extreme f(x)=2x^4-36x^2 is Minimum(-3,-162),Maximum(0,0),Minimum(3,-162)