What is the extreme f(x)=x^4-18x^2+11 ?

The extreme f(x)=x^4-18x^2+11 is Minimum(-3,-70),Maximum(0,11),Minimum(3,-70)

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extreme f(x)=x^4-18x^2+11

extreme points

f (x) = x^{4} - 18 x^{2} + 11

Minimum (- 3, - 70), Maximum (0, 11), Minimum (3, - 70)

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} + 11 : - 70

Minimum (- 3, - 70)

Plug

x = 0

into

x^{4} - 18 x^{2} + 11 : 11

Maximum (0, 11)

Plug

x = 3

into

x^{4} - 18 x^{2} + 11 : - 70

Minimum (3, - 70)

Minimum (- 3, - 70), Maximum (0, 11), Minimum (3, - 70)

f (x, y) = - 5 x^{2} y + 5 x y^{2}

f (x) = - x^{3} + 3 x^{2} + 9 x - 6

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

f (x) = x_{2} - x_{1}

3 x^{2} + 15 x + 18

What is the extreme f(x)=x^4-18x^2+11 ?
The extreme f(x)=x^4-18x^2+11 is Minimum(-3,-70),Maximum(0,11),Minimum(3,-70)