What is the tangent of f(x)= x/(x-1),\at x=0 ?

The tangent of f(x)= x/(x-1),\at x=0 is y=-x

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tangent of f(x)= x/(x-1),\at x=0

tangent of

f (x) = \frac{x}{x - 1}, at x = 0

y = - x

Solution steps

Find the tangent point:

(0, 0)

Find the slope of

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

Compute the slope of

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

x = 0 : m = - 1

Find the line with slope m=

- 1

and passing through

(0, 0) : y = - x

y = - x

(- 12, - 7), (- 8, - 4)

arctan (x)

(- 2, 3), (5, 8)

x = - 3

f (x) = x^{2} - 2 x

What is the tangent of f(x)= x/(x-1),\at x=0 ?
The tangent of f(x)= x/(x-1),\at x=0 is y=-x