Please answer All the questions FULLY!. THANKS HERO

3) The owners of a restaurant are interested analyzing the productivity of their staff. The function N(t) = 150-- 600 models the total number of customers, N, served by the V16+312 staff after t hours during an 8-hour workday (0 St s 8). Determine the rate, to the nearest tenth, at which the customers are being served at 4 hours. (A - 3 marks) 4) Determine the equation of the tangent to f(x) = -x2 +3x +1 that is perpendicular to the line y = =x+2. (1-6 marks) 5) Find numbers a, b, and c such that the graph of y = ax + bx + c has x-intercepts of 0 and 8, and a tangent with a slope of 16 at x = 2. (1 -6 marks) (more space available on next page)6. . A manufacturer of kitchen appliances experiences revenue of (C-2 marks) R(x) = 750x - - 2x3 dollars from the sale of x refrigerators per month. a. Find the marginal revenue, R'(x). b. Find the marginal revenue when 10 refrigerators per month are sold. 7. Ify = 5u' + 3u - 1 and u = 18 find x2 + 5' dx - when x = 2. (C-4 marks)e) f(x ) = 14x +5 (x2 -3) (4 -3 marks) D f ( x ) = *+1 V 3x -4 (4 - 3 marks) 2) Find the derivative of f(x)=-7x3 +5x -8 using first principles. (A -3 marks)ROUND ALL ANSWERS TO THE NEAREST TENTH, UNLESS OTHERWISE STATED. 1) Differentiate each of the following functions. Final answers should not contain negative or fraction exponents and should be simplified/factored as much as possible. a) f(x) = 4x -9x +6x +5 (K - 3 marks) b ) / (x ) = 3 (4 x 2 + 2x - 7) (K - 3 marks) 2 c) f (x) = ( 6x2 - 5)(2x -1)" (K -3 marks) d) f(x)=2+7x (K - 3 marks) (5x2 -3)