Question

The graph of a function f is given. Use the graph to find:

(a) The numbers, if any, at which f has a local maximum value. What are the local maximum values?

(b) The numbers, if any, at which f has a local minimum value. What are the local minimum values?

Short answer

Part(a) Local maximum value 1 at $x=\frac{\mathrm{\pi }}{2}$.

Part(b) Local minimum value -1 at $x=-\frac{\mathrm{\pi }}{2}$.

Step-by-step solution

Part(a)  Step 1. Given information:

The graph of function $f$:

Part(a)  Step 2. Find local maxima.

From the graph, maximum point we can notice is $\left(\frac{\mathrm{\pi }}{2},1\right)$

Therefore, local maximum value is 1 at $x=\frac{\mathrm{\pi }}{2}$.

Part(b)  Step 1. Find local minima.

From the graph, the minimum is $\left(-\frac{\mathrm{\pi }}{2},-1\right)$.

Therefore, local minimum value is -1 at$x=-\frac{\mathrm{\pi }}{2}$.