Problem Set C 1. a) Copy and complete the table below: Original Function y = 503 - 5t (z) = Inz h(x)=-5ex First derivative Second Derivative [6 marks] b) After completing the derivatives of the various functions in part 1 a) above, copy and complete the table below stating the name of EACH function that was derived: Original Function Cubic Function Logarithmic Exponential Function Function First derivative Second Derivative [4 marks] ex - 1linx + 340x5 2. Given that w(x) = 7x3 -32e* + 5Inx State the rule and explain three (3) steps that can be applied when differentiating the function w(x). [4 marks] 3. Instagram has a revenue function of R(q) = 5q2 - 10q + 600 and a cost function of C(q) = 3q2 + 200, where R(q) and C(q) are measured in thousands of dollars and q represent the number of companies who advertise on their platform measured in hundreds. Instagram has a capacity to advertise for 10000 companies in any given month on its platform. a) How much will Instagram's marginal cost be for advertising at 74% of its capacity? [2 marks] b) Calculate and interpret Instagram's marginal revenue when 8000 companies advertise with them. [3 marks] c) How many companies must advertise with Instagram so that its maximum profit can be achieved? 13 marks]