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 maximized.

(2) For the f(x)= x³ + 3x + 6, determine the coordinates of the turning point(s) and any point(s) of inflection, if they exist.