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

The extreme (-2x^2)/((x-3)(x+2)) is Maximum(-12,-48/25),Minimum(0,0)

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

extreme points

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

Maximum (- 12, - \frac{48}{25}), Minimum (0, 0)

Solution steps

f^{'} (x) = - \frac{2 ( - x ^{2} - 12 x )}{( x - 3 ) ^{2} ( x + 2 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < - 12,

Decreasing

: - 12 < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 12

into

\frac{- 2 x ^{2}}{( x - 3 ) ( x + 2 )} : - \frac{48}{25}

Maximum (- 12, - \frac{48}{25})

Plug

x = 0

into

\frac{- 2 x ^{2}}{( x - 3 ) ( x + 2 )} : 0

Minimum (0, 0)

Maximum (- 12, - \frac{48}{25}), Minimum (0, 0)

6 x + 2 y = - 2

(- 4, - 8), (1, - 5)

f (x) = 2 x - 11

\frac{3}{5} x + 25 y = 10

f (x) = x - \frac{250}{x}

What is the extreme (-2x^2)/((x-3)(x+2)) ?
The extreme (-2x^2)/((x-3)(x+2)) is Maximum(-12,-48/25),Minimum(0,0)