What is the tangent of f(x)= 6/(x-1),\at x=3 ?

The tangent of f(x)= 6/(x-1),\at x=3 is y=-3/2 x+15/2

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tangent of f(x)= 6/(x-1),\at x=3

tangent of

f (x) = \frac{6}{x - 1}, at x = 3

y = - \frac{3}{2} x + \frac{15}{2}

Solution steps

Find the tangent point:

(3, 3)

Find the slope of

f (x) = \frac{6}{x - 1} : \frac{df ( x )}{d x} = - \frac{6}{( 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{3}{2}

Find the line with slope m=

- \frac{3}{2}

and passing through

(3, 3) : y = - \frac{3}{2} x + \frac{15}{2}

y = - \frac{3}{2} x + \frac{15}{2}

What is the tangent of f(x)= 6/(x-1),\at x=3 ?
The tangent of f(x)= 6/(x-1),\at x=3 is y=-3/2 x+15/2