What is the tangent of f(x)= 2/(x-2),\at x=-4 ?

The tangent of f(x)= 2/(x-2),\at x=-4 is y=-1/18 x-5/9

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tangent of f(x)= 2/(x-2),\at x=-4

tangent of

f (x) = \frac{2}{x - 2}, at x = - 4

y = - \frac{1}{18} x - \frac{5}{9}

Solution steps

Find the tangent point:

(- 4, - \frac{1}{3})

Find the slope of

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

Compute the slope of

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

x = - 4 : m = - \frac{1}{18}

Find the line with slope m=

- \frac{1}{18}

and passing through

(- 4, - \frac{1}{3}) : y = - \frac{1}{18} x - \frac{5}{9}

y = - \frac{1}{18} x - \frac{5}{9}

x \to 0 lim (\frac{cos ( x ) - x}{x})

y = x^{3}, y = x^{\frac{1}{2}}

\frac{\partial}{\partial x} (x^{3} + 4 x^{2} + x^{4} + 3 x^{5})

\int_{0}^{6 π} x^{2} sin (2 x) d x

ln (x^{2} - 4 x + 1)

What is the tangent of f(x)= 2/(x-2),\at x=-4 ?
The tangent of f(x)= 2/(x-2),\at x=-4 is y=-1/18 x-5/9