What is the tangent of y=1+1/x ?

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

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tangent of y=1+1/x

tangent of

y = 1 + \frac{1}{x}

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

y = 1 + \frac{1}{x}

x = a_{0} : m = - \frac{1}{a _{0}^{2}}

Find the line with slope m=

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

and passing through

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

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

y = x 1 - x^{2}

x ln (x) - x

x + 1

(0, 0), (6, 3)

(- 22, 22)

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