Did you know?
Did you know that for a function of the form w(x) = Asin(Bx) + C, where A, B, and C are constants, we can determine the values of A, B, and C based on certain conditions? If the function has a maximum at (-1,7) and a minimum at (1,7), we can establish that the amplitude, A, is 7, as it represents the difference between the maximum and minimum values. Additionally, the constant term, C, is also 7 since it indicates the vertical shift of the function. By analyzing the x-values of the maximum and minimum points, we find that the phase shift, B, is π/2 or 90 degrees. Furthermore, no critical points exist between these two points, meaning the function maintains its increasing or decreasing nature throughout this interval. These insights empower us to precisely determine the formula for this specific function.
