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Unformatted text preview: MATH 140
Dr. Ellis INSTRUCTIONS: THIRD EXAM APRIL 21, 2003 1. Write your name and TA’s name on every answer sheet.
2. Answer each problem on a separate answer sheet. 3. SHOW WORK AND GIVE REASQJNS. NO CALCULATORS. [17] 1. (a) (b) [17] 2. (a) [so] 3. (a) Find the function f such that f ’(x) = 2sinx+ seczx and f(0) = 3. Find the horizontal atsymptote(s) of the graph of = 2x2+5
y 3—x2. Suppose a population is growing exponentially with
P(O) = 1,000,000 and P(2) = 2,000,000. Find P(3). Let f be continuous; on [0, 2] and differentiable on (0,2). What
does the Mean Value Theorem state about f? Let ﬂx) = 2x3 — 3x2 + 6. Find the maximum and minimum
values of f on [—1, ]. Find the area of the largest rectangle that has two sides on the
positive x axis and the positive y axis one vertex at the origin and
one vertex on the curve y = e“". Explain carefully how you know the value you found in (b) is the
maximum area. ‘ CONTINUED ON THE BACK [36] 4. Let ﬁx) = x4 + 2x3 + 1 (a) Find the intervals on which f is increasing and the intervals on
which f is decreasing. (b) Find the points (if any) at which f has relative extreme values. (0) Find the intervals onl which f is concave upward and the intervals
on which f is concave downward. (d) Find the inflection points (if any) of the graph of f. (9) Sketch the graph of f, being sure to use the information from
(a)  (d). Notice thati ﬂO) = 1 and ﬂ—3/2) = —11/16. mrh:4/O3
a:140x3ellisSpO3 ...
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 Spring '08
 Gulick

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