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KNOWLEDGE: (24 marks) APPLICATION: A complete solution is required for full marks. (18 marks) ) Differentiate each of the following. DO NOT SIMPLIFY! 2) Find an equation of the tangent line to the graph of the function f(x) = 4e* that is parallel to a) y= 7e2* +5 the line 2x -4y-5 =0. (Leave answer in exact form) b) y = 2 - In2 2 c ) f ( x ) =-er'-x 2 3) Find the absolute maximum and minimum points of the function f(x) = 3x on the interval -35x 53. (Leave answer in exact form) 6 d) y = excos(xx) 3) 4) A biologist monitoring an infestation of grubs records an initial population of 400 grubs per e) f ( x) = sinvite* hectare and, two years later, a population of 950 grubs per hectare. Use the growth equation A = a) Calculate the growth constant, k. (2) f) y = cost (5' ) of infestation. b ) Determine the instantaneous rate at which the number of grubs is increasing after 10 years 8 ) vexzer 3 c ) Determine the doubling time for the population . h) =3" (@ -5x+6) 3 1 ) y = ( sin(2x ) + e "x } d) Rewrite the growth equation, A(t), with the base of 2. 3 THINKING/INQUIRY/PROBLEM SOLVING: (10 marks) 5) Solve for x. (Leave answer in exact form) ex - 10e-* = 3 6) For what values of m does the function y = Cem* , satisfy the equation 3y" -8y' - 3y = 0 ? (Note: C and m are constants)