The demand equation for a certain commodity is given by the following equation. 1 p=EX2 24x+1728, 05x5144 Find x and the corresponding price p that maximize revenue. The maximum value of R(x) occurs at x = Some years ago it was estimated that the demand for steel approximately satised the equation p = 393 - 35x, and the total cost of producing x units of steel was C(x) = 115 + 43x. (The quantity x was measured in millions of tons and the price and total cost were measured in millions of dollars.) Determine the level of production and the corresponding price that maximize the prots. The maximum profit occurs at x = (million tons). d f()() Suppose that f(x) and g()() are differentiable functions such that f(7) = 1, f'(7) =9, g(?}=2, and g'(7) =4. Find $[] x=7I (Simplify your answer.) d f(x) aim x=7 An open rectangular box is 2 feet long and has a surface area of 12 square feet. Find the dimensions ofthe box for which the volume is as large as possible. The width of the box is feet. Find all x-coordinates of points (x,y) on the curve y = (x - 6)4 (x - 9) where the tangent line is horizontal. X=