Q. 29 - 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 3 at $x=0$.

Part(b) Local minimum value 0 at width="122" style="max-width: none; vertical-align: -5px;" $x=-2 and x=2$.

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 $\left(0,3\right).$

Therefore, local maximum value is 3 at $x=0$.

Part(b) Step 1. Find local minima.

From the graph, there are two minimum points that are $\left(-2,0\right)$ and $\left(2,0\right)$.

Therefore, local minimum value is 0 at $x=-2 and x=2$.