Name:

Directions: Show your work! Answers without justification will likely result in few points. Your written work also allows me the option of giving you partial credit in the event of an incorrect final answer (but good reasoning). Indicate clearly your answer to each problem (e.g., put a box around it). Good luck!

Problem 1 (15 pts). Below is a list of properties of function:

displaymath148

Next to the following functions, indicate all that apply from the list above to the function by placing the correct letters adjacent to the function. Give the domains of the functions as well.

  1. displaymath149

    Domain: tex2html_wrap_inline166 ; Properties: C, R

  2. displaymath150

    Domain: tex2html_wrap_inline168 ; Properties: C, O, T

  3. displaymath151

    Domain: tex2html_wrap_inline168 ; Properties: C, E, W

Problem 2 (10 pts). Sketch the derivative of the function given by the following graph:

  figure56

Problem 3 (10 pts). Carefully sketch the graph of a function which satisfies the following:

displaymath152

f is continuous, except for a jump discontinuity at x=1, and an infinite discontinuity at x=3. f is not differentiable at x=4.

Problem 4 (10 pts). Sketch the graph of the following function and use it to determine the values of a for which tex2html_wrap_inline192 exists:

displaymath153

Problem 5 (10 pts). The size of your business has grown according to the following table:

displaymath154

Graph the data, and estimate the rate of change in size at 1994 in two different ways:

Problem 6 (10 pts). Find the equation of the tangent line to the curve at the given point:

displaymath155

Problem 7 (10 pts). Evaluate the limit and justify each step by indicating the appropriate limit laws:

displaymath156

Problem 8 (25 pts). For the function f given by tex2html_wrap_inline202 do the following:

  1. Discuss the continuity and differentiability of f.
  2. Draw the graph of f on the interval [-2,4]. What is the shape of the graph of f?
  3. Use the definition of the derivative as a limit to find tex2html_wrap_inline210 .
  4. Carefully draw in the tangent line to the graph of f at x=2.
  5. Sketch in the derivative function of f based on the graph of f (carefully distinguish it from the graph of f).





LONG ANDREW E
Fri Feb 2 00:09:27 EST 2001