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

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

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

extreme points

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

Minimum (0, 0), Saddle (1, 1)

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} : 0

Minimum (0, 0)

Plug

x = 1

into

3 x^{4} - 8 x^{3} + 6 x^{2} : 1

Saddle (1, 1)

Minimum (0, 0), Saddle (1, 1)

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

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

f (x, y) = x y

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

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

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