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

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

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extreme f(x)=3x^4-4x^3-8

extreme points

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

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 0

into

3 x^{4} - 4 x^{3} - 8 : - 8

Saddle (0, - 8)

Plug

x = 1

into

3 x^{4} - 4 x^{3} - 8 : - 9

Minimum (1, - 9)

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

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