What is the extreme f(x)=(y-1)/(y^3-y+1) ?

The extreme f(x)=(y-1)/(y^3-y+1) is Saddle(0,-1),Maximum(3/2 , 4/23)

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extreme f(x)=(y-1)/(y^3-y+1)

extreme points

f (x) = \frac{y - 1}{y ^{3} - y + 1}

Saddle (0, - 1), Maximum (\frac{3}{2}, \frac{4}{23})

Solution steps

Find the critical points:

y = 0, y = \frac{3}{2}

Domain of

\frac{y - 1}{y ^{3} - y + 1} : y < - 1.32471 \dots or y > - 1.32471 \dots

Find intervals:

Increasing

: - \infty < y < - 1.32471 \dots,

Increasing

: - 1.32471 \dots < y < 0,

Increasing

: 0 < y < \frac{3}{2},

Decreasing

: \frac{3}{2} < y < \infty

Plug the extreme point

x = 0

into

\frac{y - 1}{y ^{3} - y + 1} \Rightarrow y = - 1

Saddle (0, - 1)

Plug the extreme point

x = \frac{3}{2}

into

\frac{y - 1}{y ^{3} - y + 1} \Rightarrow y = \frac{4}{23}

Maximum (\frac{3}{2}, \frac{4}{23})

Saddle (0, - 1), Maximum (\frac{3}{2}, \frac{4}{23})

f (x, y) = 2 x^{2} + 2 y^{2} - 16 x + 12 y

f (x) = x^{3} - 15 x^{2} + 63 x - 15

f (x, y) = \frac{8460}{x} + \frac{8460}{y} + 5 x y

f (x) = (85 - 0.05 x) - (600 + 35 x)

f (x) = 4 x^{2} - 24 x + 400

What is the extreme f(x)=(y-1)/(y^3-y+1) ?
The extreme f(x)=(y-1)/(y^3-y+1) is Saddle(0,-1),Maximum(3/2 , 4/23)