Evaluate. (Be sure to check by differentiating!) 5 dx, x * - 5 + 8x . . . dx = 5 + 8x (Type an exact answer. Use parentheses to clearly denote the argumentase Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 31 in. by 17 in. by cutting congruent squares from the corners and folding up the sides. Then find the volume. uni . . . The dimensions of box of maximum volume are (Round to the nearest hundredth as needed. Use a comma to separate answers as needed.) The maximum volume is (Round to the nearest hundredth as needed.)The demand, D, for a new rollerball pen is given by D = 0.006p -0.3p + 150p, where p is the price in dollars. ase a) Find the rate of change of quantity with respect to price, dD/dp. b) How many units will consumers want to buy when the price is $25 per unit? muni c) Find the rate of change at p = 25, and interpret this result. d)Would you expect dD/dp to be positive or negative? dD a dp b) units (Round to the nearest integer as needed.) c) The number of consumers who wants to buy will by when the price is $ per unit. (Round to the nearest integer as needed.) d) Would you expect dD/dp to be positive or negative? O negative O positiveEvaluate. (Be sure to check by differentiating!) dx X# - 1 + 26x 26 e tG dx 1 + 26x on (Type an exact answer. Use parentheses to clearly denote the argument of each function.) Plar & R sible