What is the extreme f(x)=210+8x^3+x^4 ?

The extreme f(x)=210+8x^3+x^4 is Minimum(-6,-222),Saddle(0,210)

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extreme f(x)=210+8x^3+x^4

extreme points

f (x) = 210 + 8 x^{3} + x^{4}

Minimum (- 6, - 222), Saddle (0, 210)

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

210 + 8 x^{3} + x^{4} : - 222

Minimum (- 6, - 222)

Plug

x = 0

into

210 + 8 x^{3} + x^{4} : 210

Saddle (0, 210)

Minimum (- 6, - 222), Saddle (0, 210)

- 6

y = 2 x^{2} - 8 x + 9

\frac{x - 2}{x - 4}

f (x) = 3 - 5 (x + 1)^{2}

x ln (x^{2})

What is the extreme f(x)=210+8x^3+x^4 ?
The extreme f(x)=210+8x^3+x^4 is Minimum(-6,-222),Saddle(0,210)