At what value of does the local max of occur?
im stuck on this part, not sure what to do after.
If a real function is differenciable then the local max (relative maximum) must occurs when
Using the Fundamental theorem,
Thus,
Thus,
Those are the possible points.
To determine what status they have we will use the first-derivative test.
Consider the three intervals,
----> ----> decreasing.
----> ----> increasing.
----> ----> decreasing.
Thus, the relative maximum occurs at
If:
then (fundamental theorem of calculus)
since the stationary points of are the roots of , which are .
To determine which is the maximum and which the minimum find at , and check the sign negative and its a maximum and positive its a minimum (the minimum is at but you had better check)
RonL