What is the tangent of f(x)=x+2/x ?

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

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tangent of f(x)=x+2/x

tangent of

f (x) = 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

f (x) = x + \frac{2}{x} : \frac{df ( x )}{d x} = 1 - \frac{2}{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{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}^{\frac{π}{2}} cos^{4} (x) d x

\int \frac{5 x + 3}{x ^{2} + 4 x + 4} d x

\frac{d}{d x} (2^{3^{x^{2}}})

\int x^{2} x^{3} + 29 d x

(1 - x^{2}) y^{^{'}} + x (y - 1) = - x^{3}

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