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}}

Compute the slope of

f (x) = \frac{x}{x - 2}

x = 1 : m = - 2

Find the line with slope m=

- 2

and passing through

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

y = - 2 x + 1

\int \frac{5 x ^{3} + 4 x}{x - 1} d x

\int \frac{x - 4}{x} d x

y^{^{'}} = \frac{7 x ^{6} e ^{\frac{y}{x}} + x ^{4} y ^{2}}{x ^{5} y}

(- 8, - 3), (- 3, 4)

f (x) = \frac{5}{x}, at 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