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

The tangent of f(x)= x/(2x-4),\at x=5 is y=-1/9 x+25/18

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

tangent of

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

y = - \frac{1}{9} x + \frac{25}{18}

Solution steps

Find the tangent point:

(5, \frac{5}{6})

Find the slope of

f (x) = \frac{x}{2 x - 4} : \frac{df ( x )}{d x} = - \frac{1}{( x - 2 ) ^{2}}

Compute the slope of

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

x = 5 : m = - \frac{1}{9}

Find the line with slope m=

- \frac{1}{9}

and passing through

(5, \frac{5}{6}) : y = - \frac{1}{9} x + \frac{25}{18}

y = - \frac{1}{9} x + \frac{25}{18}

n = 1 \sum \infty \frac{2}{1 + n ^{2}}

\frac{d}{d x} (- 2 x + 4)

\frac{1}{2 x + 3}

\frac{d}{d x} (2 + sec (x))

\frac{1}{4}

What is the tangent of f(x)= x/(2x-4),\at x=5 ?
The tangent of f(x)= x/(2x-4),\at x=5 is y=-1/9 x+25/18