Problem 56E

56. (a) If $g(x)=x^{2 / 3}$, show that $g^{\prime}(0)$ does not exist.

(b) If $a \neq 0$, find $g^{\prime}(a)$.

(c) Show that $y=x^{2 / 3}$ has a vertical tangent line at $(0,0)$.

(d) Illustrate part (c) by graphing $y=x^{2 / 3}$.

 

 

Step-by-Step Solution