What is the tangent of 3x+5/x ?

The tangent of 3x+5/x is y=(3-5/(a_{0)^2})x+(10)/(a_{0)}

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tangent of 3x+5/x

tangent of

3 x + \frac{5}{x}

y = (3 - \frac{5}{a _{0}^{2}}) x + \frac{10}{a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 3 a_{0} + \frac{5}{a _{0}})

Find the slope of

y = 3 x + \frac{5}{x} : \frac{d y}{d x} = 3 - \frac{5}{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 = 3 - \frac{5}{a _{0}^{2}}

Find the line with slope m=

3 - \frac{5}{a _{0}^{2}}

and passing through

(a_{0}, 3 a_{0} + \frac{5}{a _{0}}) : y = (3 - \frac{5}{a _{0}^{2}}) x + \frac{10}{a _{0}}

y = (3 - \frac{5}{a _{0}^{2}}) x + \frac{10}{a _{0}}

What is the tangent of 3x+5/x ?
The tangent of 3x+5/x is y=(3-5/(a_{0)^2})x+(10)/(a_{0)}