What is the tangent of 12x^{1/2} ?

The tangent of 12x^{1/2} is y= 6/(a_{0)^{1/2}}x+6a_{0}^{1/2}

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tangent of 12x^{1/2}

tangent of

12 x^{\frac{1}{2}}

y = \frac{6}{a _{0}^{\frac{1}{2}}} x + 6 a_{0}^{\frac{1}{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 12 a_{0}^{\frac{1}{2}})

Find the slope of

y = 12 x^{\frac{1}{2}} : \frac{d y}{d x} = \frac{6}{x ^{\frac{1}{2}}}

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{6}{a _{0}^{\frac{1}{2}}}

Find the line with slope m=

\frac{6}{a _{0}^{\frac{1}{2}}}

and passing through

(a_{0}, 12 a_{0}^{\frac{1}{2}}) : y = \frac{6}{a _{0}^{\frac{1}{2}}} x + 6 a_{0}^{\frac{1}{2}}

y = \frac{6}{a _{0}^{\frac{1}{2}}} x + 6 a_{0}^{\frac{1}{2}}

What is the tangent of 12x^{1/2} ?
The tangent of 12x^{1/2} is y= 6/(a_{0)^{1/2}}x+6a_{0}^{1/2}