What is the extreme (x^3-4x^2)/(x^2+1) ?

The extreme (x^3-4x^2)/(x^2+1) is Maximum(0,0),Minimum(1.51274…,-1.73088…)

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extreme (x^3-4x^2)/(x^2+1)

extreme points

\frac{x ^{3} - 4 x ^{2}}{x ^{2} + 1}

Maximum (0, 0), Minimum (1.51274 \dots, - 1.73088 \dots)

Solution steps

Find the critical points:

x = 0, x \approx 1.51274 \dots

Domain of

\frac{x ^{3} - 4 x ^{2}}{x ^{2} + 1} : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 1.51274 \dots,

Increasing

: 1.51274 \dots < x < \infty

Plug the extreme point

x = 0

into

\frac{x ^{3} - 4 x ^{2}}{x ^{2} + 1} \Rightarrow y = 0

Maximum (0, 0)

Plug the extreme point

x = 1.51274 \dots

into

\frac{x ^{3} - 4 x ^{2}}{x ^{2} + 1} \Rightarrow y = - 1.73088 \dots

Minimum (1.51274 \dots, - 1.73088 \dots)

Maximum (0, 0), Minimum (1.51274 \dots, - 1.73088 \dots)

f (x) = 10 + 5 x - x^{2}

f (x) = 2 x^{2} n x - 19 x^{2}

f (x, y, z) = - x^{2} - 3 y^{2} + 4 x - 6 y - 5

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

f (x) = 4 x + 3

What is the extreme (x^3-4x^2)/(x^2+1) ?
The extreme (x^3-4x^2)/(x^2+1) is Maximum(0,0),Minimum(1.51274…,-1.73088…)