What is the tangent of y=16sqrt(x) ?

The tangent of y=16sqrt(x) is y= 8/(sqrt(a_{0))}x+8sqrt(a_{0)}

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tangent of y=16sqrt(x)

tangent of

y = 16 x

y = \frac{8}{a _{0}} x + 8 a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 16 a_{0})

Find the slope of

y = 16 x : \frac{d y}{d x} = \frac{8}{x}

Compute the slope of

y = 16 x

x = a_{0} : m = \frac{8}{a _{0}}

Find the line with slope m=

\frac{8}{a _{0}}

and passing through

(a_{0}, 16 a_{0}) : y = \frac{8}{a _{0}} x + 8 a_{0}

y = \frac{8}{a _{0}} x + 8 a_{0}

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What is the tangent of y=16sqrt(x) ?
The tangent of y=16sqrt(x) is y= 8/(sqrt(a_{0))}x+8sqrt(a_{0)}