What is the tangent of f(x)= 1/(x-1),\at x=3 ?

The tangent of f(x)= 1/(x-1),\at x=3 is y=-1/4 x+5/4

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tangent of f(x)= 1/(x-1),\at x=3

tangent of

f (x) = \frac{1}{x - 1}, at x = 3

y = - \frac{1}{4} x + \frac{5}{4}

Solution steps

Find the tangent point:

(3, \frac{1}{2})

Find the slope of

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

Compute the slope of

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

x = 3 : m = - \frac{1}{4}

Find the line with slope m=

- \frac{1}{4}

and passing through

(3, \frac{1}{2}) : y = - \frac{1}{4} x + \frac{5}{4}

y = - \frac{1}{4} x + \frac{5}{4}

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What is the tangent of f(x)= 1/(x-1),\at x=3 ?
The tangent of f(x)= 1/(x-1),\at x=3 is y=-1/4 x+5/4