What is the tangent of y=x+2/x ?

The tangent of y=x+2/x is y=(1-2/(a_{0)^2})x+4/(a_{0)}

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tangent of y=x+2/x

tangent of

y = x + \frac{2}{x}

y = (1 - \frac{2}{a _{0}^{2}}) x + \frac{4}{a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0} + \frac{2}{a _{0}})

Find the slope of

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

Compute the slope of

y = x + \frac{2}{x}

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

Find the line with slope m=

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

and passing through

(a_{0}, a_{0} + \frac{2}{a _{0}}) : y = (1 - \frac{2}{a _{0}^{2}}) x + \frac{4}{a _{0}}

y = (1 - \frac{2}{a _{0}^{2}}) x + \frac{4}{a _{0}}

\int_{0}^{4} \frac{x}{2 x + 1} d x

x \to 0 + lim (\frac{5}{x + x ^{2}})

\frac{f ( a + h ) - f ( a - h )}{2 h}

x \to - 1 lim (∣ x - 1 ∣)

(9, - 1), (4, - 11)

What is the tangent of y=x+2/x ?
The tangent of y=x+2/x is y=(1-2/(a_{0)^2})x+4/(a_{0)}