What is the extreme f(x)=x^4+4x^3-9 ?

The extreme f(x)=x^4+4x^3-9 is Minimum(-3,-36),Saddle(0,-9)

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extreme f(x)=x^4+4x^3-9

extreme points

f (x) = x^{4} + 4 x^{3} - 9

Minimum (- 3, - 36), Saddle (0, - 9)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 3

into

x^{4} + 4 x^{3} - 9 : - 36

Minimum (- 3, - 36)

Plug

x = 0

into

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

Saddle (0, - 9)

Minimum (- 3, - 36), Saddle (0, - 9)

What is the extreme f(x)=x^4+4x^3-9 ?
The extreme f(x)=x^4+4x^3-9 is Minimum(-3,-36),Saddle(0,-9)