What is the extreme f(x)=x^4-6x^2+8x ?

The extreme f(x)=x^4-6x^2+8x is Minimum(-2,-24),Saddle(1,3)

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extreme f(x)=x^4-6x^2+8x

extreme points

f (x) = x^{4} - 6 x^{2} + 8 x

Minimum (- 2, - 24), Saddle (1, 3)

Solution steps

f^{'} (x) = 4 x^{3} - 12 x + 8

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 2

into

x^{4} - 6 x^{2} + 8 x : - 24

Minimum (- 2, - 24)

Plug

x = 1

into

x^{4} - 6 x^{2} + 8 x : 3

Saddle (1, 3)

Minimum (- 2, - 24), Saddle (1, 3)

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

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

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

f (x) = 1 + \frac{1}{x} + \frac{9}{x ^{2}} + \frac{1}{x ^{3}}

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

What is the extreme f(x)=x^4-6x^2+8x ?
The extreme f(x)=x^4-6x^2+8x is Minimum(-2,-24),Saddle(1,3)