What is the extreme f(x)=(x^3-2)/((x-1)^2) ?

The extreme f(x)=(x^3-2)/((x-1)^2) is Maximum(-1,-3/4),Saddle(2,6)

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extreme f(x)=(x^3-2)/((x-1)^2)

extreme points

f (x) = \frac{x ^{3} - 2}{( x - 1 ) ^{2}}

Maximum (- 1, - \frac{3}{4}), Saddle (2, 6)

Solution steps

f^{'} (x) = \frac{- 3 x ^{2} + x ^{3} + 4}{( x - 1 ) ^{3}}

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 1,

Increasing

: 1 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 1

into

\frac{x ^{3} - 2}{( x - 1 ) ^{2}} : - \frac{3}{4}

Maximum (- 1, - \frac{3}{4})

Plug

x = 2

into

\frac{x ^{3} - 2}{( x - 1 ) ^{2}} : 6

Saddle (2, 6)

Maximum (- 1, - \frac{3}{4}), Saddle (2, 6)

What is the extreme f(x)=(x^3-2)/((x-1)^2) ?
The extreme f(x)=(x^3-2)/((x-1)^2) is Maximum(-1,-3/4),Saddle(2,6)