Day 05 Hand In Product Rule 1) Differentiate each function using the two different methods presented below. Compare your answers in each case. a) Expand and simplify each binomial product and then differentiate using the power rule. b) Apply the product rule and then simplify. c) Apply both methods to the following functions. i) f(x) = (x+5)(2x -1) ii) h(x) = (5x - 2) (1 - 3x) iii) g(x) = (-x -1)(3x - 8) iv) f (x) = (2x - 1)(4 -2x) 2) Use the product rule to differentiate each of the following functions. a) f(x) = (5x + 2) (8x + 6) b) h(t) = (-t+4)(2t -1) c) p(x) = (2x+3)(-x-9) d) g(x) = (x- + 1)(4x + 5) e) f(x) = (1 - x)(x2 +5) f) h(t) = (+2 - 3)(3+2 + 7) 3) The fish population in a lake can be modelled by the function p(t) = 16(t2 + 30) (t + 7), where t is time, in years, from now. a) What is the current fish population? b) Determine the rate of change of the fish population in 3 years. c) Determine the rate of change of the fish population when there are 5000 fish in the lake. d) When will the fish population double from its current level? What is the rate of change in the fish population at this time