What is the tangent of f(x)= 1/(x-1),\at x=5 ?

The tangent of f(x)= 1/(x-1),\at x=5 is y=-1/16 x+9/16

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tangent of f(x)= 1/(x-1),\at x=5

tangent of

f (x) = \frac{1}{x - 1}, at x = 5

y = - \frac{1}{16} x + \frac{9}{16}

Solution steps

Find the tangent point:

(5, \frac{1}{4})

Find the slope of

f (x) = \frac{1}{x - 1} : \frac{df ( x )}{d x} = - \frac{1}{( 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{1}{16}

Find the line with slope m=

- \frac{1}{16}

and passing through

(5, \frac{1}{4}) : y = - \frac{1}{16} x + \frac{9}{16}

y = - \frac{1}{16} x + \frac{9}{16}

6 e^{- 5 x}

(8 x)^{l n (8 x)}

\frac{d}{d x} (\frac{ln ( x )}{x ^{3}})

x \to 0 lim (arcsin (x))

7 x^{4} arctan (2 x^{3})

What is the tangent of f(x)= 1/(x-1),\at x=5 ?
The tangent of f(x)= 1/(x-1),\at x=5 is y=-1/16 x+9/16