Chapter 8.4, Problem 32E

To determine

To Find: The length of the continuous function.

Answer to Problem 32E

False

Function must also be differentiable on $\left[a,b\right]$ .

Explanation of Solution

Given information: function $f(x)$ is continuous on an interval $\left[a,b\right]$ .

length of the curve is

  $L={\displaystyle \underset{a}{\overset{b}{\int }}\sqrt{1+{\left(\frac{dy}{dx}\right)}^2}}dx$

If y is a smooth function of x on $\left[a,b\right]$ .

So, Function must also be differentiable on $\left[a,b\right]$ .