1. The demand function for a good is given by the equation P = a − bQ while the total cost function is TC = dQ2 + eQ + f, where a, b, d, e and f are positive constants. (a) Derive the equation for...

1. The demand function for a good is given by the equation P = a − bQ while the total
cost function is TC = dQ2 + eQ + f, where a, b, d, e and f are positive constants.
(a) Derive the equation for profit.
(b) Derive an expression for the value of Q for which profit is maximised.
(2) For the f(x) = −x
3 + 3x + 6 determine the coordinates of the turning point(s) and
any point(s) of inflection, if they exist.