What is the extreme f(x)=3x^4+8x^3+4 ?

The extreme f(x)=3x^4+8x^3+4 is Minimum(-2,-12),Saddle(0,4)

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extreme f(x)=3x^4+8x^3+4

extreme points

f (x) = 3 x^{4} + 8 x^{3} + 4

Minimum (- 2, - 12), Saddle (0, 4)

Solution steps

f^{'} (x) = 12 x^{3} + 24 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 2

into

3 x^{4} + 8 x^{3} + 4 : - 12

Minimum (- 2, - 12)

Plug

x = 0

into

3 x^{4} + 8 x^{3} + 4 : 4

Saddle (0, 4)

Minimum (- 2, - 12), Saddle (0, 4)

What is the extreme f(x)=3x^4+8x^3+4 ?
The extreme f(x)=3x^4+8x^3+4 is Minimum(-2,-12),Saddle(0,4)