What is the extreme f(x)=x^4-4x^3+16x-16 ?

The extreme f(x)=x^4-4x^3+16x-16 is Minimum(-1,-27),Saddle(2,0)

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extreme f(x)=x^4-4x^3+16x-16

extreme

Minimum (- 1, - 27), Saddle (2, 0)

Solution steps

f^{'} (x) = 4 x^{3} - 12 x^{2} + 16

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 1

into

x^{4} - 4 x^{3} + 16 x - 16 : - 27

Minimum (- 1, - 27)

Plug

x = 2

into

x^{4} - 4 x^{3} + 16 x - 16 : 0

Saddle (2, 0)

Minimum (- 1, - 27), Saddle (2, 0)

What is the extreme f(x)=x^4-4x^3+16x-16 ?
The extreme f(x)=x^4-4x^3+16x-16 is Minimum(-1,-27),Saddle(2,0)