What is the tangent of f(x)=(x-6)/(x+2),\at x=2 ?

The tangent of f(x)=(x-6)/(x+2),\at x=2 is y= 1/2 x-2

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tangent of f(x)=(x-6)/(x+2),\at x=2

tangent of

f (x) = \frac{x - 6}{x + 2}, at x = 2

y = \frac{1}{2} x - 2

Solution steps

Find the tangent point:

(2, - 1)

Find the slope of

f (x) = \frac{x - 6}{x + 2} : \frac{df ( x )}{d x} = \frac{8}{( x + 2 ) ^{2}}

Compute the slope of

f (x) = \frac{x - 6}{x + 2}

x = 2 : m = \frac{1}{2}

Find the line with slope m=

\frac{1}{2}

and passing through

(2, - 1) : y = \frac{1}{2} x - 2

y = \frac{1}{2} x - 2

8 x - 3 x

(\frac{1}{2} - \frac{3}{2} \cdot \frac{10}{9} + 4)^{^{'}}

6 (x^{2} + y^{2}) d x + 7 x y d y = 0

\frac{d}{d x} (6 x^{2} e^{x})

x - 2, (x - 4)^{2}, x = 5

What is the tangent of f(x)=(x-6)/(x+2),\at x=2 ?
The tangent of f(x)=(x-6)/(x+2),\at x=2 is y= 1/2 x-2