The function is defined by
for all real values of x except 0.
- Find the coordinates of the points where the graph of the function meets the axes.
- Show that the function has exactly one stationary point whose lies in the interval.
- Use Newton Raphson Method to find the of the stationary point giving your answer correct to 6 decimal places. Determine the nature of the stationary point.
- Find the equations of the linear vertical and horizontal asymptotes for.
- Use your answers from 1-5 to produce a hand drawn sketch of the graph of .
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For a given firm let Q stand for the amount produced to meet a market demand. Let P stand for the price per unit of quantity produced. Assume that Q is a differentiable function of P. Let be the total revenue function and the marginal revenue.
- Give the definition of the price elasticity of demand.
Use the definition of to show that if the demand is elastic (i.e. ) then will fall if the price increases; and that if the demand is inelastic
(i.e. ) then will rise as the price increases.
- Given that . Solve the resulting differential equation to find the demand equation if when ,
- Use an expression of as a function of and to find the value of that maximises the total revenue
The supply equation is given by . Use the decimal Search method to find the equilibrium price giving your answer correct to five decimal places.
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