Consider the function #y = e^x# defined on #[-1, 2]#. What are the maximum and minimum of the function on this interval?
This function has no absolute maximum or minimum, but would have a local minimum at
We don't need calculus to explain this. The graph of any exponential function will have a domain of all the real numbers. The graph of
In calculus speak, we would say
So the local max/min will be the two end points of our closed interval. Hence there willl be a local maximum at
Hopefully this helps!