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

The extreme f(x)=(x^3)/(x+4) is Minimum(-6,108),Saddle(0,0)

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

extreme points

f (x) = \frac{x ^{3}}{x + 4}

Minimum (- 6, 108), Saddle (0, 0)

Solution steps

f^{'} (x) = \frac{2 x ^{3} + 12 x ^{2}}{( x + 4 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 6,

Increasing

: - 6 < x < - 4,

Increasing

: - 4 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 6

into

\frac{x ^{3}}{x + 4} : 108

Minimum (- 6, 108)

Plug

x = 0

into

\frac{x ^{3}}{x + 4} : 0

Saddle (0, 0)

Minimum (- 6, 108), Saddle (0, 0)

f (x) = x^{2} + 6 x + 10

f (x) = 2 x^{6} - 6 x^{4}

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

f (x) = x^{2} e^{- 3 x}

\frac{x ^{2}}{x - 8}

What is the extreme f(x)=(x^3)/(x+4) ?
The extreme f(x)=(x^3)/(x+4) is Minimum(-6,108),Saddle(0,0)