For each of the following functions in Problems 1-4:

Problem 1.

Problem 2.

Problem 3.

Problem 4.

Name _____________________________                                 Calculus                                            SHW 8

Problem 5.  The function E(T) below captures the relationship between the expansion, E, of copper and its temperature T. Note that E(T) is the ratio of two cubic polynomials in which some of  the coefficients are very small.
(a) Find the derivative of the expansion, E'(T), and make a table of values of temperature T vs E'(T), for T = 20, 50, 100, 200, 300, 400, 500, 600, 700, 800.
Note: Do not try to simplify E'(T). Just use it as is to compute values.
(b) Correctly plot the information found in (a) on the graph below.
(c) Explain in a complete sentence how E' is changing as a function of temperature.
(d) In a complete sentence, explain/describe approximately when E' is a maximum.
(e) In a complete sentence, explain/describe approximately when E' is a minimum.