What is the tangent of f(x)= 2/(x-1),\at x=4 ?

The tangent of f(x)= 2/(x-1),\at x=4 is y=-2/9 x+14/9

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tangent of f(x)= 2/(x-1),\at x=4

tangent of

f (x) = \frac{2}{x - 1}, at x = 4

y = - \frac{2}{9} x + \frac{14}{9}

Solution steps

Find the tangent point:

(4, \frac{2}{3})

Find the slope of

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

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = - \frac{2}{9}

Find the line with slope m=

- \frac{2}{9}

and passing through

(4, \frac{2}{3}) : y = - \frac{2}{9} x + \frac{14}{9}

y = - \frac{2}{9} x + \frac{14}{9}

s \to - 1 lim (\frac{1}{s ^{2} + 2 s + 1})

6 - 5 x

(\frac{( x + 11 )}{( x - 11 )})^{5}

\frac{d}{d x} (3 x - x^{2},)

y = x - 1

What is the tangent of f(x)= 2/(x-1),\at x=4 ?
The tangent of f(x)= 2/(x-1),\at x=4 is y=-2/9 x+14/9