What is the extreme x^4-12x^2+11 ?

The extreme x^4-12x^2+11 is Minimum(-sqrt(6),-25),Maximum(0,11),Minimum(sqrt(6),-25)

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extreme x^4-12x^2+11

extreme points

x^{4} - 12 x^{2} + 11

Minimum (- 6, - 25), Maximum (0, 11), Minimum (6, - 25)

Solution steps

f^{'} (x) = 4 x^{3} - 24 x

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < 0,

Decreasing

: 0 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = - 6

into

x^{4} - 12 x^{2} + 11 : - 25

Minimum (- 6, - 25)

Plug

x = 0

into

x^{4} - 12 x^{2} + 11 : 11

Maximum (0, 11)

Plug

x = 6

into

x^{4} - 12 x^{2} + 11 : - 25

Minimum (6, - 25)

Minimum (- 6, - 25), Maximum (0, 11), Minimum (6, - 25)

f (x) = x^{4} - 8 x^{3} + 1

f (x) = x^{4} - 8 x^{3} + 2

y = 2 x - 5 x^{\frac{2}{5}}

f (x) = \frac{8 + x}{8 - x} [4.7]

(1 - 2 x)^{4} (1 - x)^{2} x^{6}

What is the extreme x^4-12x^2+11 ?
The extreme x^4-12x^2+11 is Minimum(-sqrt(6),-25),Maximum(0,11),Minimum(sqrt(6),-25)