# MAT 121 - Illinois State University

```Wednesday, February 29, 2012
MAT 121
(A) For f(x) = 3x4 + 4x3 + 1, determine its absolute extreme values
over the interval [−2,1].
(B) If g(x) = x – 2√x: (i) determine its absolute extreme values over
the interval [0,9]. (ii) determine its absolute extreme values
for all x.
(C) For 2006, operating rate of factories, mines, and utilities in a
certain region of the country, expressed as a % of full capacity,
is given by the function shown below, where 0 ≤ t ≤ 250 is
measured in days. On which of the first 250 days of 2006 was
the rate the highest?
1200t
C(t) = 80 + 2
t + 40,000
Wednesday, February 29, 2012
MAT 121
2 3
2
g(x) = x - 2x - 6x + 4
3
Wednesday, February 29, 2012
MAT 121
Wednesday, February 29, 2012
MAT 121
If exactly 200 people sign up for a charter flight, Leisure World
Travel Agency charges \$400/person. However, if more than 200
people sign up for the flight (assume this is the case), then each
fare is reduced by \$1 for each additional person. Hint: Let x
denote the number of passengers above 200.
• Determine the revenue function R(x).
•
Determine how many passengers will result in a maximum
revenue for the travel agency.
•
What is the maximum revenue?
•
What would be the fare per passenger in this case?
Wednesday, February 29, 2012
MAT 121
An open-topped box is to be created from a rectangular piece of
tin that measures 20 cm by 32 cm. The box is created by removing
congruent squares from each corner of the rectangle and then
folding up the flaps.
• What is the measure of the largest square that could be
removed from each corner?
•
If each cut-out square measures x cm on each side, what is a
formula for the volume of the resulting box?
•
What value of x generates the largest volume?
•
What would be the volume in this case?
Wednesday, February 29, 2012
MAT 121
Wednesday, February 29, 2012
MAT 121
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