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

The tangent of f(x)=x+1/x ,\at x=3 is y= 8/9 x+2/3

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

tangent of

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

y = \frac{8}{9} x + \frac{2}{3}

Solution steps

Find the tangent point:

(3, \frac{10}{3})

Find the slope of

f (x) = x + \frac{1}{x} : \frac{df ( x )}{d x} = 1 - \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{8}{9}

Find the line with slope m=

\frac{8}{9}

and passing through

(3, \frac{10}{3}) : y = \frac{8}{9} x + \frac{2}{3}

y = \frac{8}{9} x + \frac{2}{3}

What is the tangent of f(x)=x+1/x ,\at x=3 ?
The tangent of f(x)=x+1/x ,\at x=3 is y= 8/9 x+2/3