Problem 55E

55. Let $f(x)=\sqrt[3]{x}$

(a) If $a \neq 0$, use Equation $2.1 .5$ to find $f^{\prime}(a)$.

(b) Show that $f^{\prime}(0)$ does not exist.

(c) Show that $y=\sqrt[3]{x}$ has a vertical tangent line at $(0,0)$. (Recall the shape of the graph of $f$. See Figure 1.2.13.)

 

Step-by-Step Solution