Q. 32 - Precalculus Enhanced with Graphing Utilities

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?

Step-by-Step Solution

Answer

Part(a) Local maximum value 1 at $x=0$.

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

Part(a) Step 1. Given information:

The graph of function is:

Part(a) Step 2. Find local maxima.

From the graph, maximum point we can notice is $\left(0,1\right)$.

Therefore, local maximum value is 1 at $x=0$.

Part(b) Step 1. Find local minima.

From the graph, there are two minimum points that are $\left(-\mathrm{\pi },-1\right) and \left(\mathrm{\pi },-1\right)$.

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