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

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

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

extreme

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)

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