MT1186: The demand equation for a market is given by: q(1 + 2 ln p) = 2. Show that the elasticity of demand is equal to the: Mathematical Methods Assignment, SIM, Singapore

Questions

• The demand equation for a market is given by:
  q(1 + 2 ln p) = 2

(a) Show that the elasticity of demand is equal to the inverse demand function.

(b) Hence, determine the range of values of p such that the elasticity of demand will be elastic.

• Let for values of x where it is defined.

(a) Find all the x and y-intercept of the curve y = f(x).

(b) Find all the horizontal and vertical asymptotes of the curve y = f(x).

(c) Find and classify all the stationary points of f(x).

(d) Sketch the curve y = f(x).

• Show that the function f is given by
  f(x, y) = y² − 4xy + 4x² + x²y²,
  has just one stationary point, and classifies it.