What is the tangent of f(x)=(-5)/(x-1),\at a=8 ?

The tangent of f(x)=(-5)/(x-1),\at a=8 is y= 5/((a-1)^2)x+(-10a+5)/((a-1)^2)

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tangent of f(x)=(-5)/(x-1),\at a=8

tangent of

f (x) = \frac{- 5}{x - 1}, at a = 8

y = \frac{5}{( a - 1 ) ^{2}} x + \frac{- 10 a + 5}{( a - 1 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a

Find the tangent point:

(a, - \frac{5}{a - 1})

Find the slope of

f (x) = \frac{- 5}{x - 1} : \frac{df ( x )}{d x} = \frac{5}{( x - 1 ) ^{2}}

Compute the slope of

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

x = a : m = \frac{5}{( a - 1 ) ^{2}}

Find the line with slope m=

\frac{5}{( a - 1 ) ^{2}}

and passing through

(a, - \frac{5}{a - 1}) : y = \frac{5}{( a - 1 ) ^{2}} x + \frac{- 10 a + 5}{( a - 1 ) ^{2}}

y = \frac{5}{( a - 1 ) ^{2}} x + \frac{- 10 a + 5}{( a - 1 ) ^{2}}

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What is the tangent of f(x)=(-5)/(x-1),\at a=8 ?
The tangent of f(x)=(-5)/(x-1),\at a=8 is y= 5/((a-1)^2)x+(-10a+5)/((a-1)^2)