Chapter 6.5, Problem 8QR

To determine

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

Answer to Problem 8QR

Concave up

Explanation of Solution

Given:

  $y=\cos xon\left[0,\pi \right]$

Calculation:

  $\begin{array}{c}y\text{'}=-\cos x\cot x\\ y"=-{\csc }^{3}x+\csc x{\cot }^{2}x\end{array}$

Since $y">0$ for all $x\in \left[0,\pi \right]$ , the curve is concave up.