P(x)=1.4875(10)x-0.016x³ +0.485x²-2.5x thousand dollars gives the weekly profit, in thousand dollars, x weeks from the start of a fiscal year, 0≤x≤52. Checkpoint: P(2) = -3.18562 a. Sketch the slope graph of P. b. Find the derivative of P. Include the output units. 50 40 30 +P(x) thousand dollars c. Sketch the slope graph of P'. d. Find the second derivative of P. Include the output units. e. Mark an "X" directly on the function curve of Pat each at the inflection points. Then draw vertical lines that connects the inflection points of P to the corresponding slopes on P' and to the corresponding values on P". What is the value of P" at each of the inflection points on P? f. Name the approximate interval in which P is concave down. Are values of P" positive or negative on that interval? g. Find the following for the inflection point in which the profit is increasing most rapidly on the given interval, correct to three decimal places. P(x)=. P"(x)= P'(x)=. -20 10 x weeks 8 12 16 20 24 28 32 36 40 44 48 52 Pix) thousand dollars per week 12 16 20 24 28 32 36 40 44 48 52 weeks P) thousand dollars per week per week xw 4 8 12 16 20 24 28 32 36 40 44 48 h. Use part g) to fill in the blanks. Over the given one-year period, the business's weekly profit was increasing most rapidly weeks after the fiscal year began, when the business's weekly profit was thousand dollars and was increasing by. thousand dollars per week.