What is the tangent of x^{1/3} ?

The tangent of x^{1/3} is y= 1/(3a_{0)^{2/3}}x+a_{0}^{1/3}-(a_{0}^{1/3})/3

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tangent of x^{1/3}

tangent of

x^{\frac{1}{3}}

y = \frac{1}{3 a _{0}^{\frac{2}{3}}} x + a_{0}^{\frac{1}{3}} - \frac{a _{0}^{\frac{1}{3}}}{3}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{\frac{1}{3}})

Find the slope of

y = x^{\frac{1}{3}} : \frac{d y}{d x} = \frac{1}{3 x ^{\frac{2}{3}}}

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{1}{3 a _{0}^{\frac{2}{3}}}

Find the line with slope m=

\frac{1}{3 a _{0}^{\frac{2}{3}}}

and passing through

(a_{0}, a_{0}^{\frac{1}{3}}) : y = \frac{1}{3 a _{0}^{\frac{2}{3}}} x + a_{0}^{\frac{1}{3}} - \frac{a _{0}^{\frac{1}{3}}}{3}

y = \frac{1}{3 a _{0}^{\frac{2}{3}}} x + a_{0}^{\frac{1}{3}} - \frac{a _{0}^{\frac{1}{3}}}{3}

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What is the tangent of x^{1/3} ?
The tangent of x^{1/3} is y= 1/(3a_{0)^{2/3}}x+a_{0}^{1/3}-(a_{0}^{1/3})/3