# Thread: Local & Global Extrema at the same points

1. ## Local & Global Extrema at the same points

The following question is on our test, I know you can have a global and local max or min at the same point, but I am unsure about the question given at hand. I am pretty sure you cannot have a local min and global max at the same point and vice-versa.

Here is the question:

2. (a) We have already seen that a local extrema may also be a global extrema. For example, for
f(x) = x2 over the interval I = [��1; 1], x = 0 is the local and global minimum. Is it possible for a local minimum to be a global maximum? Similarly, is it possible for a local maximum to be a global minimum? Why or why not? Give a clear argument to support your response. Give an example supporting your thesis.

(b) Give an example of a function that does not satisfy the Mean Value Theorem. State those properties of the function that do not allow the MVT to be applied to this particular function

Any help would be kindly appreciated.

2. For b,
f(x) = |x| where $\displaystyle x \in [-1,1]$
Differentiability fails