A monopolist faces the negatively-sloped inverse demand functionP(Q).

a) Write the revenue functionR(Q)and derive the rst-order condition formaximum revenue.

(b) Derive the second-order condition. Can you verify that the second-order condition for a maximum revenue is satisfied?

(c) (4 points) Suppose now that the inverse demand function is P(Q) =Q2Q+ 1.Find the revenue maximizing output Q and the associated maximum revenue R(Q)(apply all necessary and sufficient conditions, and economic notions).(d) As seen in class, an inflexion point is when the second derivative of a function has value zero. Find the inflexion point(s) of the revenue function defined in (c).(e) Graph the revenue function from part (c) indicating all the extrema points, all the zeros and the inflexion point(s), as well as the value of the function at each point. On your graph, you may use either analytical number (fractions and roots) or rounded numbers at three decimal places.