Q. 30 - 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 2 at $x=0$.

Part(b) Local minimum value 0 at $x=-1 and x=1$.

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 $(0,2)$.

Therefore, local maximum value is 2 at $x=0$.

Part(b) Step 1. Find local minima.

From the graph, there are two minimum points which are $\left(-1,0\right) and (1,0)$.

Therefore, local minimum value is 0 at $x=-1 and x=1$.