What is the tangent of-1/x ,\at x=3 ?

The tangent of-1/x ,\at x=3 is y= 1/9 x-2/3

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tangent of-1/x ,\at x=3

tangent of

- \frac{1}{x}, at x = 3

y = \frac{1}{9} x - \frac{2}{3}

Solution steps

Find the tangent point:

(3, - \frac{1}{3})

Find the slope of

y = - \frac{1}{x} : \frac{d y}{d x} = \frac{1}{x ^{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}{9}

Find the line with slope m=

\frac{1}{9}

and passing through

(3, - \frac{1}{3}) : y = \frac{1}{9} x - \frac{2}{3}

y = \frac{1}{9} x - \frac{2}{3}

What is the tangent of-1/x ,\at x=3 ?
The tangent of-1/x ,\at x=3 is y= 1/9 x-2/3