4.4 Continued
1. Find the absolute max and absolute min of
f(x) = 3x
4
 4 x
3
+4 on [1,5]
2. If f(x) = x/ (x
2
+ 4) on [1,4],
Then f’(x) =  (x2)(x+2)/( x
2
+ 4)
2
.
•
Find the absolute maximum
•
Find the absolute minimum
3. Find the absolute max and absolute min of f(x) = 7x
2
+ 7 x – 5
4. A watch company is marketing a new highend watch.
The
demand function is given by
p= 360 – (1/3)x
2
for 0<
x<
20 Where p is the price in dollars and x is
the number of units sold at price p.
•
The cost function for producing x units per day is C(x) = 100 +
216x.
•
Therefore, the profit function is
P(x) = 144x – (1/3)x
3
– 100.
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How many watches should be produced
each day to
maximize profit?
4.5 Guidelines for Solving Optimization
Problems
•
1. Assign a letter to each variable mentioned
in the problem.
If appropriate, draw and
label a figure.
•
2. Find an expression for the quantity to be
optimized
•
3. Use the conditions given in the problem to
write the quantity to be optimized as a
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 Spring '08
 VAUGHN
 Calculus, Optimization, maximum revenue, absolute min, Rancho Los Feliz

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