What is the extreme f(x)=6x^4+24x^3 ?

The extreme f(x)=6x^4+24x^3 is Minimum(-3,-162),Saddle(0,0)

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extreme f(x)=6x^4+24x^3

extreme points

f (x) = 6 x^{4} + 24 x^{3}

Minimum (- 3, - 162), Saddle (0, 0)

Solution steps

f^{'} (x) = 24 x^{3} + 72 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 3

into

6 x^{4} + 24 x^{3} : - 162

Minimum (- 3, - 162)

Plug

x = 0

into

6 x^{4} + 24 x^{3} : 0

Saddle (0, 0)

Minimum (- 3, - 162), Saddle (0, 0)

What is the extreme f(x)=6x^4+24x^3 ?
The extreme f(x)=6x^4+24x^3 is Minimum(-3,-162),Saddle(0,0)