Page 1 MTH 241 Differentiation practice, business models LAB H NAME: SHOW ALL WORK! Use another sheet of paper if you need more space 1. A company knows that x units of a product will sell at a price of p dollars per unit. The function p(x) outputs the per unit price in dollars for an input of the number of units sold, x The solution to which of the following equations could find the number of units, x , that will maximize the revenue for this company? a) x . p'(x) + p(x) -0 b ) p'( x ) = 0 *. P'(x) -P(x) =0 x 2 d) p"(x) = 0 e) x . p(x) = 0 2. The total cost of producing x units for a company can be modeled by the function C(x). where C(x) is in dollars. The solution to which of the following equations could find the number of units, x, that will minimize the average cost of production? a) x . C'(x) + C(x) =0 b ) C' (x ) = 0 x . C' (x) - C(x) x 2 d) C"(x) =0 C(x) e ) -=0 - xPage 2 3) For questions a-f. first state which, if any. of the following differentiation rules you need to use If more than one needs to be used, specify the order. Use the product rule, quotient rule and or chain rule to differentiate each of the following functions a ) b(x ) = 3x* + 6Vx-3 b) r(7) = 71 - 12 (16-151) c) s(x) _ 14x - 3x2 + 2 7VX' - x+45\fPage 4. Given the graph of the first derivative of her) - determine the function h(x) 's intervals of increase, decrease and concavity J - h(x) 5. Given the graph of the first derivative of g(x) dg determine the function g(x)'s intervals of increase, decrease and concavity 7 - 8 (x) E. Find the equation of the line tangent to the graph of the function r(x) = (2x -2) (Vx +2)? at the point where x - 1