What is the tangent of f(x)= 5/x ,\at x=3 ?

The tangent of f(x)= 5/x ,\at x=3 is y=-5/9 x+10/3

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tangent of f(x)= 5/x ,\at x=3

tangent of

f (x) = \frac{5}{x}, at x = 3

y = - \frac{5}{9} x + \frac{10}{3}

Solution steps

Find the tangent point:

(3, \frac{5}{3})

Find the slope of

f (x) = \frac{5}{x} : \frac{df ( x )}{d x} = - \frac{5}{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{5}{9}

Find the line with slope m=

- \frac{5}{9}

and passing through

(3, \frac{5}{3}) : y = - \frac{5}{9} x + \frac{10}{3}

y = - \frac{5}{9} x + \frac{10}{3}

What is the tangent of f(x)= 5/x ,\at x=3 ?
The tangent of f(x)= 5/x ,\at x=3 is y=-5/9 x+10/3