Chapter 6.5, Problem 4QR

To determine

To find: that the curve is concave up or concave down on the given interval.

Answer to Problem 4QR

Concave down

Explanation of Solution

Given:

  $y=\sin \left(\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)on\left[48\pi ,50\pi \right]$

Calculation:

  $\begin{array}{c}y\text{'}=\frac{1}{2}\cos \frac{x}{2}\\ y"=-\frac{1}{4}\sin \frac{x}{2}\end{array}$

Since $y"\le 0$ for all $x\in \left[48\pi ,50\pi \right]$ , the curve is concave down.