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Stewart_Calc_7ET ch04sec01
MULTIPLE CHOICE
1. Find the absolute maximum value of .
a.
5
b.
15
c.
d.
e.
0
2. Estimate the extreme values of the function.
a.
b.
c.
d.
e.
3. Find all the critical numbers of the function.
a.
b.
c.
d.
e.
None of these
4. Find the critical number(s), if any, of the function
a.
b.
–4
c.
d.
5. Find the critical number(s), if any of the function
a.
b.
0,
c.
d.
0,
6. Find the critical number(s), if any, of the function .
a.
b.
c.
d.
None of these
7. Find the critical number(s), if any, of the function .
a.
b.
and
c.
d.
and
8. Find the critical number(s), if any, of the function
a.
b.
c.
d.
1
2
1
2
1
2
1
1
1
9. Find the absolute maximum and absolute minimum values, if any, of the function
on [0, 25]
a.
Abs. max.
abs. min.
b.
Abs. max.
abs. min.
c.
Abs. max.
abs. min.
d.
Abs. max.
abs. min.
10. Find the absolute maximum and absolute minimum values, if any, of the function
on .
a.
Abs. max.
abs. min.
b.
Abs. max.
abs. min.
c.
Abs. max.
abs. min.
d.
Abs. max.
abs. min.
11. Find the critical numbers of .
a.
0, 3,
b.
0, 2,
c.
d.
0, 3,
e.
0, 2,
12. Find the absolute maximum value of on the interval .
a.
8
b.
5
c.
7
d.
6
e.
4
13. Find any absolute or local maximum and minimum values of if .
a.
is an absolute maximum
b.
– 4 is a local maximum
c.
– 4 is an absolute minimum
d.
6 is an absolute maximum
e.
6 is an absolute minimum
f.
6 is a local minimum
NUMERIC RESPONSE
1. Find the absolute maximum value of y = on the interval .
2. Find the local and absolute extreme values of the function on the given interval.
,
3. Estimate the absolute minimum value of the function to two decimal places
on the interval .
__________
4. Find the critical numbers of the function.
1 2 3 4 5 6 7 8–1–2–3–4–5–6–7–8 x
1
2
3
4
5
6
7
8
–1
–2
–3
–4
–5
–6
–7
–8
y
5. Find all the critical numbers of the function.
6. Find the absolute maximum of the function.
on the interval
7. Estimate the absolute maximum value of the function to two decimal places
on the interval .
8. Find the absolute minimum value(s) of on the interval [0, 6].
9. Find all the maximum and minimum values of the function.
10. Find the maximum and minimum points of the function.
SHORT ANSWER
1. The graph below is the graph of function f on the interval Find the absolute
maximum and absolute minimum values of f (if they exist) and where they are attained.
1 2 3 4–1–2–3–4 x
1
2
3
4
–1
–2
–3
–4
y
2. Sketch the graph of on and find its absolute maximum and absolute
minimum values, if any.
3. Sketch the graph of on and find its absolute maximum and absolute
minimum values, if any.
4. Sketch the graph of the function on and find its absolute maximum and
absolute minimum values, if any.
5. Find the absolute maximum and absolute minimum values, if any, of the function
on
6. Find the absolute maximum and absolute minimum values, if any, of the function
on .
7. The quantity demanded per month of an item is related to the unit price by the demand
equation
,
where p is measured in dollars and x is measured in units of a thousand. How many items
must be sold by the manufacturer to maximize its revenue?
Hint: Recall that the revenue is given by
8. A cylindrical tank of height 16 feet is filled with water. Suppose a jet of water flows through
an orifice on the tank. It can be shown that the range R (in feet) of the jet of water is given
by
.
Where should the orifice be located so that the jet of water will have the maximum range?
