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

The tangent of f(x)= 2/(x-1),\at x=-2 is y=-2/9 x-10/9

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

tangent of

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

y = - \frac{2}{9} x - \frac{10}{9}

Solution steps

Find the tangent point:

(- 2, - \frac{2}{3})

Find the slope of

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

Compute the slope of

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

x = - 2 : m = - \frac{2}{9}

Find the line with slope m=

- \frac{2}{9}

and passing through

(- 2, - \frac{2}{3}) : y = - \frac{2}{9} x - \frac{10}{9}

y = - \frac{2}{9} x - \frac{10}{9}

\int \frac{x ( x - 1 )}{2} d x

x \to 0 lim (1 + sin^{2} (3 x))

\frac{d ^{2}}{d x ^{2}} (sin (x) cos (x))

\int (\frac{( x - 3 )}{( x + 2 )}) d x

\frac{\partial}{\partial x} (9)

What is the tangent of f(x)= 2/(x-1),\at x=-2 ?
The tangent of f(x)= 2/(x-1),\at x=-2 is y=-2/9 x-10/9