What is the tangent of 3sqrt(x) ?

The tangent of 3sqrt(x) is y= 3/(2sqrt(a_{0))}x+3sqrt(a_{0)}-(3sqrt(a_{0)})/2

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tangent of 3sqrt(x)

tangent of

3 x

y = \frac{3}{2 a _{0}} x + 3 a_{0} - \frac{3 a _{0}}{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 3 a_{0})

Find the slope of

y = 3 x : \frac{d y}{d x} = \frac{3}{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{3}{2 a _{0}}

Find the line with slope m=

\frac{3}{2 a _{0}}

and passing through

(a_{0}, 3 a_{0}) : y = \frac{3}{2 a _{0}} x + 3 a_{0} - \frac{3 a _{0}}{2}

y = \frac{3}{2 a _{0}} x + 3 a_{0} - \frac{3 a _{0}}{2}

What is the tangent of 3sqrt(x) ?
The tangent of 3sqrt(x) is y= 3/(2sqrt(a_{0))}x+3sqrt(a_{0)}-(3sqrt(a_{0)})/2