What is the extreme f(x)=3x^4-12x^3 ?

The extreme f(x)=3x^4-12x^3 is Saddle(0,0),Minimum(3,-81)

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extreme f(x)=3x^4-12x^3

extreme

Saddle (0, 0), Minimum (3, - 81)

Solution steps

f^{'} (x) = 12 x^{3} - 36 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

3 x^{4} - 12 x^{3} : 0

Saddle (0, 0)

Plug

x = 3

into

3 x^{4} - 12 x^{3} : - 81

Minimum (3, - 81)

Saddle (0, 0), Minimum (3, - 81)

What is the extreme f(x)=3x^4-12x^3 ?
The extreme f(x)=3x^4-12x^3 is Saddle(0,0),Minimum(3,-81)