Arrington A1.(30 pts.) Find the derivatives of the following functions (you need not simplify): (a) f(x) = )xln(3e)xln()x3( (b) f(x) = e)4xln(6 4. (c) f(x)= x)xln(32 - )x3e(xe2. (5 pts.) The population of a certain country t years from now is predicted to be P(t) = 2 )100t(e million people. Find its instantaneous and relative rates of change at this time (t=0).Arrington A3. (15 pts.) An open-top box is to be made from a square sheet of cardboard 12 inches on each side by cutting a square from each corner and folding up the sides as shown in the diagrams below. Find the volume of the largest box that can be made this way.Arrington A4. (20 pts.)).1x2(66x12)x(fand);1x)(2x(612x6x6)x(f 12x;3x 2x- f(x)223 (a) Find the critical numbers and the inflection points of f. (b) Construct sign charts for the first and second derivatives. (c) Find all open intervals of increase and decrease and open intervals on which the graph is concave up and concave down. (d) Classify each critical point as a relative maximum, relative minimum or neither. (e) Sketch the graph of y = f(x) by hand, using and labeling only the relative extreme points, the inflection points and the y-intercept. Note that f(-2) =4 , f(-1) = -7, f(-)21= -5, f)21(= 6.5, f(1)= 13, and f(2) = 20.Arrington A5. (10 pts.) When a management training company prices its seminar on management at $1000 per person, 20 people will attend the seminar. For each $50 reduction in the price, the company estimates that an additional 2 people will attend. How much should the company charge for the seminar to maximize its revenue?6. (10 pts.) .13yxy2x323 Find dxdy at x = 2 and y = 1.Arrington A7.(10 pts.) A demand function is given by D(p) = p2e. Find E(5), the elasticity of demand at p =
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