Question

Write an expression for the x-values where the the maximum in the expression occurs:
y=6cos((2pi/14)x)-2

I know that the maximum occurs every 14 units if you start at 0,0. I'm stuck after that.

Answer 1

since you labelled this "pre-calculus" , I suppose we can't use the derivative, which would be the easiest way of doing it

consider: y = 6 cos( (2π/14)x)
the period = 2π/(2π/14) = 14
You had that.
so we have a cosine curve with a max of 6 when x = 0 and when x = 14
but we are dropping the whole curve by 2 units, so the maximum will be 4
so the max occurs at
x = 0 , ±14, ±28, ±42, etc , that is every 14 units

general solution:
max of 4 occurs when x = 14k, where k is an integer.

Answer 2

Thanks! Great explanation.