The following questions are a calculus review. If you master them then the level of calculus used in the class should not be a problem for you.

If you feel you need more practice, check the the following questions. If you just need a little bit of help click here for a short calculus review.

• f(x)=x²/(1+4x)
• f(x)=ln(x+20) (recall that the derivative of ln(x) is 1/x).
• f(x)=ln(x+a) where a is a fixed number.
  Note that if you choose a=20 the answer of both this question and the previous one must be the same.
• f(x)=(4+x⁴)^1/2
  Note that (...)^1/2 is the same as the square root of (...).
• f(x)=(a+x⁴)^1/2 where a is a fixed number.
  Choose a=4 to check your answer.
• f(x)=3x²+6x⁴.
• f(x)=ax²+bx⁴ where a and b are fixed numbers.
  Choose a=3 and b=6 to check your answer.

Note that if you take a partial derivative of a function with respect to one variable then you treat all other variable as if they were fixed numbers (i.e., in the questions above with numbers a or b you have essentially already taken a partial derivative).

• f(x,y)=xy³
• f(x,y)=x+20y
• f(x,y)=10ln(x)+ln(y).
• f(x,y)=(x+2y)/y.
  
• f(x,y)=2x²+y.
• f(x,y)=ax²+by where a and b are fixed numbers.
  Again, check your answer for a=2 and b=1

Question 3: The following exercises will be useful for graphing indifference curves.

• Assume that x²y=20.
  • Write y as a function of x.
  • Graph the function for x>=0, where x is graphed on the horizontal axis, and y on the vertical axis.
  • Determine the slope at x=2.
  • Determine the value of y at x=2.
• Now assume that the function is given by xy²=36.
  • Again write y as a function of x.
  • Graph the function for x>=0, where x is graphed on the horizontal axis, and y on the vertical axis.
  • Determine the slope at x=4.
  • Determine the value of y at x=4.

To the title page