What is the tangent of 6sqrt(x) ?

The tangent of 6sqrt(x) is y= 3/(sqrt(a_{0))}x+3sqrt(a_{0)}

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tangent of 6sqrt(x)

tangent of

6 x

y = \frac{3}{a _{0}} x + 3 a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 6 a_{0})

Find the slope of

y = 6 x : \frac{d y}{d x} = \frac{3}{x}

Compute the slope of

y = 6 x

x = a_{0} : m = \frac{3}{a _{0}}

Find the line with slope m=

\frac{3}{a _{0}}

and passing through

(a_{0}, 6 a_{0}) : y = \frac{3}{a _{0}} x + 3 a_{0}

y = \frac{3}{a _{0}} x + 3 a_{0}

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What is the tangent of 6sqrt(x) ?
The tangent of 6sqrt(x) is y= 3/(sqrt(a_{0))}x+3sqrt(a_{0)}