What is the tangent of y=sqrt(x)(81.9) ?

The tangent of y=sqrt(x)(81.9) is y=(40.95)/(sqrt(a_{0))}x+(819sqrt(a_{0)})/(20)

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tangent of y=sqrt(x)(81.9)

tangent of

y = x (81.9)

y = \frac{40.95}{a _{0}} x + \frac{819 a _{0}}{20}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0} \cdot 81.9)

Find the slope of

y = x 81.9 : \frac{d y}{d x} = \frac{40.95}{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{40.95}{a _{0}}

Find the line with slope m=

\frac{40.95}{a _{0}}

and passing through

(a_{0}, a_{0} 81.9) : y = \frac{40.95}{a _{0}} x + \frac{819 a _{0}}{20}

y = \frac{40.95}{a _{0}} x + \frac{819 a _{0}}{20}

What is the tangent of y=sqrt(x)(81.9) ?
The tangent of y=sqrt(x)(81.9) is y=(40.95)/(sqrt(a_{0))}x+(819sqrt(a_{0)})/(20)