Application (12 marks) 7. The base, b, and height, h, of a triangle are represented by b = (x + 3)2 and h = (x2 + 3). Determine the rate of change of the area of the triangle when x = 3. (5 marks) A = 1 bh " The AROC is the derivative - 1 x + 3 ) ( x ) + 3 ) of it and it is iso AROC = 1 | ( x + 3 ) ( 8 x ) + ( x " + 3 ) 10 ( x + 3 ) ( 1) ] sub in * = 3 - [ ( 3 + 3 ) ( 8 ( 3) ) + ( ( 3) # + 3 ) @ ( 3 + 3 ) ] AROC = 180 8. An ice-cream company estimates that the cost, C, in dollars of producing x tubs of ice-cream is C(x) = 0.0001x2 + 1.75x + 4100. The revenue, R, in dollars from selling x tubs of ice-cream is R(x ) = 6.50x. a) Determine the marginal cost of producing 4000 tubs of ice-cream. (2 marks) Marginal cost - c'(x ) ( ( x ) = 0. 000 8 x 1:75 ( ( 40 00 ) = 0.0-008 ( 40 0 0 ) + 1. 75 ( = 2.5 5) b) Determine the marginal profit from selling 4000 tubs of ice-cream. (3 marks) Marginal Profit - R - C P (X ) = R ( x ) - ( ( x ) P( x2 : - 0. 00 03 xth. 75 = 6. 50x - (0. cool x + 1. 75 x + 9 100) ' Sub in 9008 P ' (4000 ) : - 0.000 7 ( 40 00 ) 14.75 P (x ) = - 0. 00 01 x 2 + 4 - 75 x + 910 03 ( = 3.95) c) What is the selling price of a tub of ice-cream? Explain. (2 marks ) R ( x ) = 6 . 50x The revenue is the price times The amount of tubs So 6.50 ( 1 ) 2 6 . 5 dollars) Page 4 of 4