What is the extreme f(x)=200+8x^3+x^4 ?

The extreme f(x)=200+8x^3+x^4 is Minimum(-6,-232),Saddle(0,200)

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extreme f(x)=200+8x^3+x^4

extreme points

f (x) = 200 + 8 x^{3} + x^{4}

Minimum (- 6, - 232), Saddle (0, 200)

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

200 + 8 x^{3} + x^{4} : - 232

Minimum (- 6, - 232)

Plug

x = 0

into

200 + 8 x^{3} + x^{4} : 200

Saddle (0, 200)

Minimum (- 6, - 232), Saddle (0, 200)

What is the extreme f(x)=200+8x^3+x^4 ?
The extreme f(x)=200+8x^3+x^4 is Minimum(-6,-232),Saddle(0,200)