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

The tangent of f(x)=(2x)/(x-1),\at x=2 is y=-2x+8

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

tangent of

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

y = - 2 x + 8

Solution steps

Find the tangent point:

(2, 4)

Find the slope of

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

Compute the slope of

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

x = 2 : m = - 2

Find the line with slope m=

- 2

and passing through

(2, 4) : y = - 2 x + 8

y = - 2 x + 8

\int (x^{2} + 1) e^{2 x} d x

f (x) = 5 e^{x}

\frac{d}{d x} (\frac{3}{4} x^{\frac{3}{2}})

\frac{1}{( 3 x ) ^{2}}

x \to 2 lim (3 x^{2} + 7 x - 1)

What is the tangent of f(x)=(2x)/(x-1),\at x=2 ?
The tangent of f(x)=(2x)/(x-1),\at x=2 is y=-2x+8