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

The extreme f(x,y)=x^4-8x^3+22x^2-24x is Minimum(1,-9),Maximum(2,-8),Minimum(3,-9)

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

extreme points

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

Minimum (1, - 9), Maximum (2, - 8), Minimum (3, - 9)

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 : - 9

Minimum (1, - 9)

Plug

x = 2

into

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

Maximum (2, - 8)

Plug

x = 3

into

x^{4} - 8 x^{3} + 22 x^{2} - 24 x : - 9

Minimum (3, - 9)

Minimum (1, - 9), Maximum (2, - 8), Minimum (3, - 9)

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

f (x, y) = x^{2} + y^{3} - 300 x - 75 y - 3

0.285 x^{2} - 2.28 x + 7.6

f (x) = x ln (\frac{x}{4})

x^{4 - 50 x^{2}}

What is the extreme f(x,y)=x^4-8x^3+22x^2-24x ?
The extreme f(x,y)=x^4-8x^3+22x^2-24x is Minimum(1,-9),Maximum(2,-8),Minimum(3,-9)