What is the extreme f(x)=x^4-18x^2-3 ?

The extreme f(x)=x^4-18x^2-3 is Minimum(-3,-84),Maximum(0,-3),Minimum(3,-84)

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extreme f(x)=x^4-18x^2-3

extreme points

f (x) = x^{4} - 18 x^{2} - 3

Minimum (- 3, - 84), Maximum (0, - 3), Minimum (3, - 84)

Solution steps

f^{'} (x) = 4 x^{3} - 36 x

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 3

into

x^{4} - 18 x^{2} - 3 : - 84

Minimum (- 3, - 84)

Plug

x = 0

into

x^{4} - 18 x^{2} - 3 : - 3

Maximum (0, - 3)

Plug

x = 3

into

x^{4} - 18 x^{2} - 3 : - 84

Minimum (3, - 84)

Minimum (- 3, - 84), Maximum (0, - 3), Minimum (3, - 84)

f (x) = 13 + 2 x - x^{2}, 0 \leq x \leq 5

f (x) = x^{4} - 18 x^{2} + 5

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

f (x) = - 2 (x - 3) (x + 5)

x^{3} - 2 x^{2} - 15 x + 5, - 2 \leq x \leq 0

What is the extreme f(x)=x^4-18x^2-3 ?
The extreme f(x)=x^4-18x^2-3 is Minimum(-3,-84),Maximum(0,-3),Minimum(3,-84)