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

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

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

tangent of

f (x) = 2 x + x

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 2 a_{0} + a_{0})

Find the slope of

f (x) = 2 x + x : \frac{df ( x )}{d x} = 2 + \frac{1}{2 x}

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 = 2 + \frac{1}{2 a _{0}}

Find the line with slope m=

2 + \frac{1}{2 a _{0}}

and passing through

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

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

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