MATH 1100: QUANTITATIVE ANALYSIS
TEST #2 (VERSION A)
Name:
This test has 4 pages and 4 problems.
No calculators are allowed. You are permitted only a pencil or pen. Work out
everything as far as you can before making decimal approximations.
1. Find the derivative with respect to x of
1/3
y = x2 + 1
.
Date: September 24, 2001.
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MATH 1100: QUANTITATIVE ANALYSIS
2. Find the tangent line to the curve
y = x5 − x3
at x = 1.
TEST #2 (VERSION A)
MATH 1100: QUANTITATIVE ANALYSIS
TEST #2 (VERSION A)
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3. The response y of the body to an amount x of adrenalin is given by
x
y=
a + bx
where a and b are constants determined by experiment.
(a) Where is this function continuous?
(b) Suppose that for any x ≥ 0 the value of y can not be negative. What
can you say about a and b? Explain your answer. (For example, are
they both positive, both negative, or of opposite signs?)
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MATH 1100: QUANTITATIVE ANALYSIS
TEST #2 (VERSION A)
4. A product has sales S (in millions of dollars) given as a function of time t
(in months) by
1
S =1+
.
(t + 1)5
(a) Find the rate of change of sales at time t = 1.
(b) Find the second derivative of sales at t = 1, and use it to explain how
the rate of sales is changing at t = 1.