What is the tangent of 4/x ,\at x=3 ?

The tangent of 4/x ,\at x=3 is y=-4/9 x+8/3

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tangent of 4/x ,\at x=3

tangent of

\frac{4}{x}, at x = 3

y = - \frac{4}{9} x + \frac{8}{3}

Solution steps

Find the tangent point:

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

Find the slope of

y = \frac{4}{x} : \frac{d y}{d x} = - \frac{4}{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{4}{9}

Find the line with slope m=

- \frac{4}{9}

and passing through

(3, \frac{4}{3}) : y = - \frac{4}{9} x + \frac{8}{3}

y = - \frac{4}{9} x + \frac{8}{3}

What is the tangent of 4/x ,\at x=3 ?
The tangent of 4/x ,\at x=3 is y=-4/9 x+8/3