What is the tangent of x+1/x ?

The tangent of x+1/x is y=(1-1/(a_{0)^2})x+2/(a_{0)}

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tangent of x+1/x

tangent of

x + \frac{1}{x}

y = (1 - \frac{1}{a _{0}^{2}}) x + \frac{2}{a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0} + \frac{1}{a _{0}})

Find the slope of

y = x + \frac{1}{x} : \frac{d y}{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 = 1 - \frac{1}{a _{0}^{2}}

Find the line with slope m=

1 - \frac{1}{a _{0}^{2}}

and passing through

(a_{0}, a_{0} + \frac{1}{a _{0}}) : y = (1 - \frac{1}{a _{0}^{2}}) x + \frac{2}{a _{0}}

y = (1 - \frac{1}{a _{0}^{2}}) x + \frac{2}{a _{0}}

What is the tangent of x+1/x ?
The tangent of x+1/x is y=(1-1/(a_{0)^2})x+2/(a_{0)}