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Exercise 7.1 Use differentiation to find the stationary point of the following quadratic functions and determine whether it is a local maximum or a local minimum using (a) the rst derivative test and (h) the second derivative test. i. r] = 3:r2 + 6.1". _ 20-, ii. g(;'] = 3:2 + a: + 20. Verify your answers Irv completing the square. Exercise 7.2 Find the stationary points of the followii'ig functions and determine whether they are a local numimum, a local minimum or neither of these. In each case, determine whether any of the points you haVe found are global. 3 3 23:2 + 31' 15; ii. 9(a) : 2.13 + 3:1".2 + 121' 6. i. x) : Exercise 7.3 A rm has a. monopoly on its market and so it can decide the price at which it sells its product. If it sells the product for price p, then demand is given by the equation q = 300 2;) where q is the amount. sold. The cost. of producing q is given by the function cu } '11\" + 30 \"'2 . = 1L f _ . I I 10. and the revenue is given by the function R(q) = pg. i. Find the revenue function, Rm}. in terms of r; and hence nd the prot function. 7r(q)._ in terms of q. ii. Calculate the value of q that will give the rm its maximum prot making sure that you check that this value of or does indeed give you the maximum prot. What is the maximum prot that the rm makes and Wl'iat price, p, will provide this? iii. If the rm can produce at. most 120 units, what. price will maximise the prot':J