What is the extreme f(x)=5(1/(x-4)-1/(x+2)) ?

The extreme f(x)=5(1/(x-4)-1/(x+2)) is Maximum(1,-10/3)

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extreme f(x)=5(1/(x-4)-1/(x+2))

extreme points

f (x) = 5 (\frac{1}{x - 4} - \frac{1}{x + 2})

Maximum (1, - \frac{10}{3})

Solution steps

f^{'} (x) = \frac{5 ( - 12 x + 12 )}{( x - 4 ) ^{2} ( x + 2 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 1,

Decreasing

: 1 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = 1

into

5 (\frac{1}{x - 4} - \frac{1}{x + 2}) : - \frac{10}{3}

Maximum (1, - \frac{10}{3})

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

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}

What is the extreme f(x)=5(1/(x-4)-1/(x+2)) ?
The extreme f(x)=5(1/(x-4)-1/(x+2)) is Maximum(1,-10/3)