What is the extreme f(x)=230+8x^3+x^4 ?

The extreme f(x)=230+8x^3+x^4 is Minimum(-6,-202),Saddle(0,230)

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extreme f(x)=230+8x^3+x^4

extreme points

f (x) = 230 + 8 x^{3} + x^{4}

Minimum (- 6, - 202), Saddle (0, 230)

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

230 + 8 x^{3} + x^{4} : - 202

Minimum (- 6, - 202)

Plug

x = 0

into

230 + 8 x^{3} + x^{4} : 230

Saddle (0, 230)

Minimum (- 6, - 202), Saddle (0, 230)

f (x, y) = e^{- (x^{2} + y^{2})} (x^{2} + 2 y^{2})

\frac{ln ( 4 x )}{x}

f (x) = \frac{4}{x - 3}

f (x, y) = x^{2} + 2 y^{2} + 2 x - 3

f (x) = 19 + 4 x - x^{2}

What is the extreme f(x)=230+8x^3+x^4 ?
The extreme f(x)=230+8x^3+x^4 is Minimum(-6,-202),Saddle(0,230)