Write your answers to these problems on blank paper (see Guidelines for Written Work in Canvas) and
turn them in on Canvas (same guidelines as Written Homework 1).
1. a) In Written Homework 2 problem 1.i) you found that the slope of C(q) at q = 100 is approximately
5.015. What is the exact slope of C(q) = 75 + 2q + .015q
2 at q = 100?
b) What is the slope of C(q) at q = 50?
c) Cʺ(q) = ________________________.
d) C(q) is concave _______ (up, down). This means as q increases, the Marginal Cost of producing the
next widget is __________ (increasing, decreasing, the same). This means that the cost to produce the
100th widget is _________ (more, less, the same) as the cost to produce the 50th widget.
e) In general, you would prefer to be a producer who has a concave ________ (up, down) cost function.
2. True or False:
a) If fʺ(6) = 0 we can conclude that f has an inflection point at 6.
b) If f′(-3) = 0 we can conclude that the line tangent to f at -3 is flat.
c) f(x) = √x + 3 has a first derivative function that is defined for all x values in the domain of f.
3. Do exercise 56 from page 98 of the textbook.
4. Do exercise 58a from page 98 of the textbook.
5. Do exercise 76 from page 101 of the textbook.