demand equation

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 MT1186 Mathematical Methods 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.