f(x)=A sin(b(x-c))+d
we have to find the values of A,b,c,d and have been given the points (4,6) (62,6)
we also know that f'(33)=0 and f'(4)=2/3
any help would be appreciated
We have four unknowns and four conditions. The first two conditions you can simply plug in:
6 = A sin ( b (4-c)) + d
6 = A sin (b (62-c)) + d
For the two derivative conditions, you first find the derivative:
f' = A cos (b (x-c)) b (by the chain rule)
... can you finish the rest?
Good luck!