What is the tangent of f(x)= 2/(x-5),\at x=7 ?

The tangent of f(x)= 2/(x-5),\at x=7 is y=-1/2 x+9/2

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tangent of f(x)= 2/(x-5),\at x=7

tangent of

f (x) = \frac{2}{x - 5}, at x = 7

y = - \frac{1}{2} x + \frac{9}{2}

Solution steps

Find the tangent point:

(7, 1)

Find the slope of

f (x) = \frac{2}{x - 5} : \frac{df ( x )}{d x} = - \frac{2}{( x - 5 ) ^{2}}

Compute the slope of

f (x) = \frac{2}{x - 5}

x = 7 : m = - \frac{1}{2}

Find the line with slope m=

- \frac{1}{2}

and passing through

(7, 1) : y = - \frac{1}{2} x + \frac{9}{2}

y = - \frac{1}{2} x + \frac{9}{2}

\int (x^{2} + 1) (4 x - 3) d x

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

\int x^{5} 6 x^{6} + 2 d x

\int (4 x^{2} + 3)^{2} d x

x^{2} - x, 2 x - 2 x^{2}

What is the tangent of f(x)= 2/(x-5),\at x=7 ?
The tangent of f(x)= 2/(x-5),\at x=7 is y=-1/2 x+9/2