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

The tangent of y= 1/(x-2),\at x=4 is y=-1/4 x+3/2

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

tangent of

y = \frac{1}{x - 2}, at x = 4

y = - \frac{1}{4} x + \frac{3}{2}

Solution steps

Find the tangent point:

(4, \frac{1}{2})

Find the slope of

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

Find the line with slope m=

- \frac{1}{4}

and passing through

(4, \frac{1}{2}) : y = - \frac{1}{4} x + \frac{3}{2}

y = - \frac{1}{4} x + \frac{3}{2}

What is the tangent of y= 1/(x-2),\at x=4 ?
The tangent of y= 1/(x-2),\at x=4 is y=-1/4 x+3/2