What is the extreme f(x)=3x^4-8x^3+6x^2-9 ?

The extreme f(x)=3x^4-8x^3+6x^2-9 is Minimum(0,-9),Saddle(1,-8)

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extreme f(x)=3x^4-8x^3+6x^2-9

extreme points

f (x) = 3 x^{4} - 8 x^{3} + 6 x^{2} - 9

Minimum (0, - 9), Saddle (1, - 8)

Solution steps

f^{'} (x) = 12 x^{3} - 24 x^{2} + 12 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 0

into

3 x^{4} - 8 x^{3} + 6 x^{2} - 9 : - 9

Minimum (0, - 9)

Plug

x = 1

into

3 x^{4} - 8 x^{3} + 6 x^{2} - 9 : - 8

Saddle (1, - 8)

Minimum (0, - 9), Saddle (1, - 8)

f (x, y) = 7 x^{2} y + 9 x y^{2}

- 4 x^{3} + 200 x^{2} - 3000 x + 17000

f (x) = - x + 10

f (x) = - 5 t^{2} + 61 t + 18

f (x, y) = x^{2} + y^{2} - 30

What is the extreme f(x)=3x^4-8x^3+6x^2-9 ?
The extreme f(x)=3x^4-8x^3+6x^2-9 is Minimum(0,-9),Saddle(1,-8)