What is the extreme g(x)=6x^4+32x^3 ?

The extreme g(x)=6x^4+32x^3 is Minimum(-4,-512),Saddle(0,0)

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extreme g(x)=6x^4+32x^3

extreme points

g (x) = 6 x^{4} + 32 x^{3}

Minimum (- 4, - 512), Saddle (0, 0)

Solution steps

f^{'} (x) = 24 x^{3} + 96 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 4,

Increasing

: - 4 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 4

into

6 x^{4} + 32 x^{3} : - 512

Minimum (- 4, - 512)

Plug

x = 0

into

6 x^{4} + 32 x^{3} : 0

Saddle (0, 0)

Minimum (- 4, - 512), Saddle (0, 0)

What is the extreme g(x)=6x^4+32x^3 ?
The extreme g(x)=6x^4+32x^3 is Minimum(-4,-512),Saddle(0,0)