What is the extreme f(x)=x^4-12x^3-29 ?

The extreme f(x)=x^4-12x^3-29 is Saddle(0,-29),Minimum(9,-2216)

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extreme f(x)=x^4-12x^3-29

extreme points

f (x) = x^{4} - 12 x^{3} - 29

Saddle (0, - 29), Minimum (9, - 2216)

Solution steps

f^{'} (x) = 4 x^{3} - 36 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 9,

Increasing

: 9 < x < \infty

Plug

x = 0

into

x^{4} - 12 x^{3} - 29 : - 29

Saddle (0, - 29)

Plug

x = 9

into

x^{4} - 12 x^{3} - 29 : - 2216

Minimum (9, - 2216)

Saddle (0, - 29), Minimum (9, - 2216)

What is the extreme f(x)=x^4-12x^3-29 ?
The extreme f(x)=x^4-12x^3-29 is Saddle(0,-29),Minimum(9,-2216)