Question

find a formula for a function of the form y=Asin(Bx)+C with a minimum at (1.5,9), a maximum at (4.5,-3) and no critical points between these two points.
y=?

Answer 1

\[y'' is +ve at x = 1.5, -ve at x +4.5\]

\[so y'' = -AB^2sinBx +ve\]

so Bx in 3rd or 4th quadrant, as sin must be -ve

Answer 2

1.5B in 3rd or 4th quadrant, 4.5B in first or second.

Answer 3

Mmmm...getting a bit lost. I'll try again later if no one comes up with a solution.