What is the tangent of f(x)= 1/(x-1),\at x=-4 ?

The tangent of f(x)= 1/(x-1),\at x=-4 is y=-1/25 x-9/25

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tangent of f(x)= 1/(x-1),\at x=-4

tangent of

f (x) = \frac{1}{x - 1}, at x = - 4

y = - \frac{1}{25} x - \frac{9}{25}

Solution steps

Find the tangent point:

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

Find the slope of

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

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = - \frac{1}{25}

Find the line with slope m=

- \frac{1}{25}

and passing through

(- 4, - \frac{1}{5}) : y = - \frac{1}{25} x - \frac{9}{25}

y = - \frac{1}{25} x - \frac{9}{25}

What is the tangent of f(x)= 1/(x-1),\at x=-4 ?
The tangent of f(x)= 1/(x-1),\at x=-4 is y=-1/25 x-9/25