MHF4U1 Derivatives Assignment 1. A health food store sells 1000 protein bars each month for $3.00 each. The manager estimates sales will increase by 60 bars for each $0.50 decrease in price. a) Find the demand function in terms of the number of protein bars sold, x. b) Find the revenue function. c) Find the marginal revenue function. d) Find the marginal revenue when 1500 bars are sold. What does this number represent? /4t /3a At his hot dog stand, Andrew usually sells 175 hot dogs per day at $3.50 each. His research tells him that for every $0.25 decrease in price of a hot dog, he will sell 10 more hot dogs per day. a) Determine the revenue function R in terms of the number of $0.25 decreases in price, n. b) Determine the marginal revenue function. c) Evaluate R'(10) and explain its meaning d) Sketch the graph of R(x) using graphing technology and copy the graph into your notes. La_bel the axes and the important points. Based on the graph, what is the maximum profit? How much Andrew should charge for one hot dog to maximize the profit. e) Solve equation R'=O. f) How can Andrew use the answers from cl) and e) in his business? /5a A particle moves along a horizontal line so that its position at any positive time t is given by the . 1 . . . . function s(t) = t3 - 4t2 + 15t + 2, where 5 IS In meters and t IS In seconds. a) Find the velocity and acceleration functions. b) At what values oft does the particle change direction. Justify your answer. c) What is the position of the particle at t = 0? d) In what direction is the particle moving at the beginning of its movement (from t = 0 to the first time the particle changes direction)? Justify your answer. e) Is the particle slowing down or speeding up at t = 25? Explain. /9a