What is the tangent of f(x)=5sqrt(x) ?

The tangent of f(x)=5sqrt(x) is y= 5/(2sqrt(a_{0))}x+5sqrt(a_{0)}-(5sqrt(a_{0)})/2

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tangent of f(x)=5sqrt(x)

tangent of

f (x) = 5 x

y = \frac{5}{2 a _{0}} x + 5 a_{0} - \frac{5 a _{0}}{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 5 a_{0})

Find the slope of

f (x) = 5 x : \frac{df ( x )}{d x} = \frac{5}{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 = \frac{5}{2 a _{0}}

Find the line with slope m=

\frac{5}{2 a _{0}}

and passing through

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

y = \frac{5}{2 a _{0}} x + 5 a_{0} - \frac{5 a _{0}}{2}

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