Chapter 4.2, Problem 60E

To determine

To predict: The statement is true or false.

Answer to Problem 60E

The statement is True.

Explanation of Solution

Given Information: The slope of $y=\sqrt[3]{x}$ is $\frac{1}{3x^{\frac{2}{3}}}$ .

Calculation:

The slope of the curve $y=\sqrt[3]{x}$ is,

  $\begin{array}{c}y=\sqrt[3]{x}\\ \frac{dy}{dx}=\frac{1}{3}{x}^{\frac{1}{3}-1}\\ =\frac{1}{3}{x}^{\frac{-2}{3}}\\ =\frac{1}{3x^{\frac{2}{3}}}\end{array}$

The statement is True.