Find the coordinates of the minimum/maximum of the curve: Y = 8X - 2X^2 - 9, and determine whether it is a maximum or a minimum.

First we need to find the derivative of the curve:dy/dx = 8 - 4X.We can then find the X coordinate by setting this equal to zero: 0 = 8 - 4X, X = 2.Plugging this back into the original equation gives us the Y coordinate: Y = 8(2) - 2(2)² - 9 = -1, Y = -1.Therefore the coordinates of the point are (2, -1)We know that this point must be a maximum as the coefficient of X² is negative and therefore the curve is n shaped.