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Math 150a Midterm #3. April 29, 2005
Attention! Please, note that this is the closed book test. You are not allowed to use graphing
calculator. Simple calculators are allowed. Please, show all important steps in you solution but do
not make your solution excessively long.
1. (15pt) Find the two numbers, x and y, such that xy = 36, and the value of
x2
+ y2
is a minimum.
2
2. Sketch the graph of the function f(x) following the steps listed below:
f(x) = ln(x2
+ 1).
a)(3pt) specify the domain;
b)(5pt) specify the intervals of increasing and decreasing, list critical points;
c)(5pt) specify the intervals where the function is concave up and concave down, list
inflection points;
