Homework SourseFor the following equation is there a difference between the
For the following equation is there a difference between the local max/min and the global max/min? As far as I can tell the max and mins will always be at the same value of P(t).
P(t)=2-3cos((pi*t)/6)
Because it is a repeating function they should be the same unless I am missing something.
Thank you!
P(t)=2-3cos((pi*t)/6)
Because it is a repeating function they should be the same unless I am missing something.
Thank you!
Solution
Yes, you are correct, the maximum value P(t) can obtain is 5 and the minimum value is -1. If we just look at a region of the domain of P(t) we can\'t say that we have found the global max/min because there are an infinite number of points with these same values, (so we can\'t call this point at t = 0 THE global minimum, for example) Just because a point is the lowest the function ever gets, doesn\'t mean that it is the global minimum. So, you are correct, there is no lower value than -1 and there is no higher point than 5. On the other hand, there are an infinite number of points with P(t) = 5, so we wouldn\'t be telling the whole story if we said P(6) is the location of the global maximum.
