Originally Posted by
killer786 
well im having quite alot of trouble doing questions like these could someone give me some insight into how they should be done thank you!
A function f(x) is known to be of the form F(x)=Acos(px+q) + B. It has a local maximum at (6, 8) and the next local minimum is at (10, 2). Find the constants A, p, q and B and hence give the formula for the function.
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has a maximum value
when
and a minimum value
when
Since there are multiple maxima and minima, there will be multiple values of
and
. Below, I've taken the first (and most obvious) values.
varies between
and
. Since these maximum and minimum values are 8 and 2 respectively, we get:
The maximum occurs when. So, from what I said above, the simplest value is:
The minimum is when(1)
. So:
So the formula we want is:, from (1)
and
