Chapter 8, Problem 29RE

To determine

To find : the distance does it take to travel from the local maximum to the local minimum.

Answer to Problem 29RE

It takes to travel this distance is $2.296$ sec.

Explanation of Solution

Given information : A particle travels at $2$ units per second along the curve $y=x^3-3x^2+2$ .

Calculation :

The local maximum occurs at $x=0$ and the local minimum occurs at $x=2$ .

The total distance travelled by the particle is given by:

  $\begin{array}{l}{\displaystyle \underset{0}{\overset{2}{\int }}\sqrt{1+{\left(\frac{d}{dx}\left(x^3-3x^2+2\right)\right)}^2}}dx\\ \Rightarrow 4.592\end{array}$

The particle is moving at $2$ units per second, the time it takes to travel this distance is $\raisebox{1ex}{$4.592$}\!\left/ \!\raisebox{-1ex}{$2$}\right.=2.296\sec$ .