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

The extreme-x/((x-1)(x-3)^2) is Minimum(-1,-1/32),Maximum(3/2 ,-4/3)

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

extreme points

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

Minimum (- 1, - \frac{1}{32}), Maximum (\frac{3}{2}, - \frac{4}{3})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Increasing

: 1 < x < \frac{3}{2},

Decreasing

: \frac{3}{2} < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 1

into

- \frac{x}{( x - 1 ) ( x - 3 ) ^{2}} : - \frac{1}{32}

Minimum (- 1, - \frac{1}{32})

Plug

x = \frac{3}{2}

into

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

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

Minimum (- 1, - \frac{1}{32}), Maximum (\frac{3}{2}, - \frac{4}{3})

x^{2} - 4 x [- 1.4]

f (x) = - x^{4} + 2 x^{2} y - \frac{1}{2} y^{2} - 4 y + 12

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

f (x) = 2 x^{4} - 8 x

4 x^{3} - 12 x^{2} + 8 x

What is the extreme-x/((x-1)(x-3)^2) ?
The extreme-x/((x-1)(x-3)^2) is Minimum(-1,-1/32),Maximum(3/2 ,-4/3)