Could someone complete this? I would like to compare my answers to those of a tutor.

MATH 1171: Calculus for Business and Management Sciences A21 Assignment 2: Differentiation Techniques (80 marks total) Your mark will be given as a percentage. [10 marks] (5 marks) (5 marks) [10 marks] (5 marks) (5 marks) [10 marks] (5 marks) (5 marks) [10 marks] (6 marks) (4 marks) [10 marks] Find the derivative in each case. You need not simplify your answer. a. f(t) = (t2 %)(t3 + 3J2). b. g(t) = f;- Find the derivative in each case. Simplify your answer. a. f(x) = (3x2 1)4(5 2906. b.f(x) = 3):: Find an equation of the tangent line to the graph of: a. f(x) = V2363 + 7x atx = 1. b. 906) = 3x+2 xl )zatx=2. For the function f(x) = 2x3 73c2 + 2436 + 11, a. Give all the points where the tangent line is horizontal. Note a point is given by two co-ordinates (_ , _). Give exact values. b. Give an equation of the tangent line at each of these points. Give exact values. Find y(4)(x) fory = 31: TRU Open Learning A22 [10 marks] 6. (3 marks) (3 marks) (4 marks) [10 marks] 7. (6 marks) (4 marks) [10 marks] 8. Assignment 2: Differentiation Techniques Suppose that the number of items sold after t months is modelled by 500t a. Find N'(6) and N'(12). b. Find N"(6), N"(12). c. What do the answers in a. and b. tell you about NOE)? Letf(x) = iand g(x) = W 1. Let h(x) = fog. a. Find h'(x). b. Find h'(8). A company determines the cost, in thousands of dollars for producing x items is given by 606) = \\./500952 x + 75. If it plans to boost production in t months from now according to the function x(t) = 301\" + 7, how fast will the costs be rising 6 months from now? TRU Open Learning