What is the extreme f(x)=x^4-8x^3+22x^2-24x+8 ?

The extreme f(x)=x^4-8x^3+22x^2-24x+8 is Minimum(1,-1),Maximum(2,0),Minimum(3,-1)

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extreme f(x)=x^4-8x^3+22x^2-24x+8

extreme points

f (x) = x^{4} - 8 x^{3} + 22 x^{2} - 24 x + 8

Minimum (1, - 1), Maximum (2, 0), Minimum (3, - 1)

Solution steps

f^{'} (x) = 4 x^{3} - 24 x^{2} + 44 x - 24

Find intervals:

Decreasing

: - \infty < x < 1,

Increasing

: 1 < x < 2,

Decreasing

: 2 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 1

into

x^{4} - 8 x^{3} + 22 x^{2} - 24 x + 8 : - 1

Minimum (1, - 1)

Plug

x = 2

into

x^{4} - 8 x^{3} + 22 x^{2} - 24 x + 8 : 0

Maximum (2, 0)

Plug

x = 3

into

x^{4} - 8 x^{3} + 22 x^{2} - 24 x + 8 : - 1

Minimum (3, - 1)

Minimum (1, - 1), Maximum (2, 0), Minimum (3, - 1)

x^{3} - 2 x^{2} - 2

f (x) = 168000 - 200 x

2 x y

f (x) = \frac{x}{5 x + 4}, 7 \leq x \leq 13

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

What is the extreme f(x)=x^4-8x^3+22x^2-24x+8 ?
The extreme f(x)=x^4-8x^3+22x^2-24x+8 is Minimum(1,-1),Maximum(2,0),Minimum(3,-1)