Question

4. Find the exact area of the closed region bounded by y=25 - x² and y=o between x = -6 and x= 1 5. The cost for x items. is c(x) = 5x² - 99 dollars, and the revenue for x items is R(x) = 8x² + 4x dollars. Find the rate at which the average profit is changing when 600 items are produced and sold.

Answer 1

The given arrre y = 25-22 25 .1 5 The area between x=-6 and x=25 bounded by ya 25-x and y=0 is (25-x²) de

[25 258 23151 .6 - 25.0 +78 16 3 16 3 se writ Area between x=-5 and a=1 bounded by y-25-27 and y=0 is -5 (25-29 34 23 252 - -5 + 3 250 3 sq - 108 unit i Area bonded by the region aurre y = 25-8² and yao between x=-6 and x=1 is = 113 1/3 sq unit is 16+108 3

6 Cost for x item CCM) = 5x²ggx dollars is for x item R(x) = 8x² + 4 5x dollares ro Revenue 2 va Profit = R(x) = C(2) P. (a) = 8x² + 4x - 5x²7 ggr. Rate Change of profit P'(x) = 24x² + ·lox +99 The rate at which the average profit is Chringing When 600 item are produced and sold P (600) 8634099.08 dollan UD