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

The extreme f(x)=x^4+8x^3+3 is Minimum(-6,-429),Saddle(0,3)

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

extreme

Minimum (- 6, - 429), Saddle (0, 3)

Solution steps

f^{'} (x) = 4 x^{3} + 24 x^{2}

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 6

into

x^{4} + 8 x^{3} + 3 : - 429

Minimum (- 6, - 429)

Plug

x = 0

into

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

Saddle (0, 3)

Minimum (- 6, - 429), Saddle (0, 3)

What is the extreme f(x)=x^4+8x^3+3 ?
The extreme f(x)=x^4+8x^3+3 is Minimum(-6,-429),Saddle(0,3)