Question

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

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

Answer 1

Step 1:

The function has local maximum at , since for all close to , .

The local maximum value is .

Step 2:

The function has local minimum at and , since for all close to , .

The local minimum value is  .

Also for all close to ,

The local minimum value is .

The local minimum values are and .

Solution:

The local maximum value is .

The local minimum values are and .