What is the tangent of f(x)= x/(x-2),\at x=1 ?

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

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tangent of f(x)= x/(x-2),\at x=1

tangent of

f (x) = \frac{x}{x - 2}, at x = 1

y = - 2 x + 1

Solution steps

Find the tangent point:

(1, - 1)

Find the slope of

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

Find the line with slope m=

- 2

and passing through

(1, - 1) : y = - 2 x + 1

y = - 2 x + 1

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