Problems for seminar #1, are all taken from the exam problem collection, except the last which is just quoted below:


* You will need:
 - recall the definition of inflection point, which is where f'' changes sign.
 - the intermediate value theorem, which will be given in the Monday 5th lecture: If f is continuous on [a,b] and f(a)<0<f(b), then it hits f(c)=0 for some c in [a,b].


* Problems:
 - From the compendium: 18, 32, 36, 117.
 - Let F(x,y) = x exp(y) be a production function defined for nonnegative x,y. Consider a level curve F(x,y)=C, C>0, on which y is a function of x.
   Then y can be solved explicitely as y= ln C - ln x, but in problems (a)--(c) you are asked to NOT solve this way, but use the implicit calculations rules:
      (a) Compute the MRS = - dy/dx on this level curve using implicit differentiation.
      (b) Compute the elasticity of y wrt. x
      (c) Compute the elasticity of substitution of F by using the fomula in the book
      (d) Verify your answers in (a)--(c) by calculating in a different manner (in (a), (b) use the form y = ln C - ln x, while in (c) calculate the ratio d ln (y/x) / d ln MRS.