What is the extreme f(x)=250+8x^3+x^4 ?

The extreme f(x)=250+8x^3+x^4 is Minimum(-6,-182),Saddle(0,250)

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extreme f(x)=250+8x^3+x^4

extreme

Minimum (- 6, - 182), Saddle (0, 250)

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

250 + 8 x^{3} + x^{4} : - 182

Minimum (- 6, - 182)

Plug

x = 0

into

250 + 8 x^{3} + x^{4} : 250

Saddle (0, 250)

Minimum (- 6, - 182), Saddle (0, 250)

What is the extreme f(x)=250+8x^3+x^4 ?
The extreme f(x)=250+8x^3+x^4 is Minimum(-6,-182),Saddle(0,250)