What is the extreme f(x)=(x^3+9)/(x^2+4) ?

The extreme f(x)=(x^3+9)/(x^2+4) is Maximum(0, 9/4),Minimum(1.31185…,1.96778…)

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extreme f(x)=(x^3+9)/(x^2+4)

extreme points

f (x) = \frac{x ^{3} + 9}{x ^{2} + 4}

Maximum (0, \frac{9}{4}), Minimum (1.31185 \dots, 1.96778 \dots)

Solution steps

Find the critical points:

x = 0, x \approx 1.31185 \dots

Domain of

\frac{x ^{3} + 9}{x ^{2} + 4} : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1.31185 \dots,

Increasing

: 1.31185 \dots < x < \infty

Plug the extreme point

x = 0

into

\frac{x ^{3} + 9}{x ^{2} + 4} \Rightarrow y = \frac{9}{4}

Maximum (0, \frac{9}{4})

Plug the extreme point

x = 1.31185 \dots

into

\frac{x ^{3} + 9}{x ^{2} + 4} \Rightarrow y = 1.96778 \dots

Minimum (1.31185 \dots, 1.96778 \dots)

Maximum (0, \frac{9}{4}), Minimum (1.31185 \dots, 1.96778 \dots)

f (x, y) = 2 x^{3} - 9 x^{2} + 12 x + 2 y^{3} + 3 y^{2}

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

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

f (x) = 2 x^{2} + 2 x y

f (x, y) = 5 x^{2} - 3 y^{2} + 4 x y - 32 x + 10 y

What is the extreme f(x)=(x^3+9)/(x^2+4) ?
The extreme f(x)=(x^3+9)/(x^2+4) is Maximum(0, 9/4),Minimum(1.31185…,1.96778…)