What is the tangent of f(x)= 2/(x-6),\at x=8 ?

The tangent of f(x)= 2/(x-6),\at x=8 is y=-1/2 x+5

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tangent of f(x)= 2/(x-6),\at x=8

tangent of

f (x) = \frac{2}{x - 6}, at x = 8

y = - \frac{1}{2} x + 5

Solution steps

Find the tangent point:

(8, 1)

Find the slope of

f (x) = \frac{2}{x - 6} : \frac{df ( x )}{d x} = - \frac{2}{( x - 6 ) ^{2}}

Compute the slope of

f (x) = \frac{2}{x - 6}

x = 8 : m = - \frac{1}{2}

Find the line with slope m=

- \frac{1}{2}

and passing through

(8, 1) : y = - \frac{1}{2} x + 5

y = - \frac{1}{2} x + 5

\int_{2}^{5} \frac{x}{x ^{2} + 4 x + 20} d x

(x^{2} - 16 x + 64) (x^{2} + 64 x + 4)

\int \frac{sec ( \frac{1}{x} )}{x ^{2}} d x

\frac{d y}{d x} = (\frac{x - y}{x})

(cos (5 x))^{^{'}}

What is the tangent of f(x)= 2/(x-6),\at x=8 ?
The tangent of f(x)= 2/(x-6),\at x=8 is y=-1/2 x+5