What is the tangent of f(x)= 5/(x-2),\at x=4 ?

The tangent of f(x)= 5/(x-2),\at x=4 is y=-5/4 x+15/2

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tangent of f(x)= 5/(x-2),\at x=4

tangent of

f (x) = \frac{5}{x - 2}, at x = 4

y = - \frac{5}{4} x + \frac{15}{2}

Solution steps

Find the tangent point:

(4, \frac{5}{2})

Find the slope of

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

Compute the slope of

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

x = 4 : m = - \frac{5}{4}

Find the line with slope m=

- \frac{5}{4}

and passing through

(4, \frac{5}{2}) : y = - \frac{5}{4} x + \frac{15}{2}

y = - \frac{5}{4} x + \frac{15}{2}

\int tan^{2} (7 x) d x

\int_{1}^{2} 12 x^{2} 4^{x^{3}} d x

- 5 sin (2 t)

e^{- x + 1} - e^{- x + 1} x

x \to 3 lim (\frac{1 - 2 x}{x - 3})

What is the tangent of f(x)= 5/(x-2),\at x=4 ?
The tangent of f(x)= 5/(x-2),\at x=4 is y=-5/4 x+15/2