For Exercises 41-42, a table of values is given for Y 1 = f x . Determine whether the intermediate value theorem guarantees that the function has a zero on the given interval. Y 1 = 10 x 4 + 21 x 3 − 119 x 2 − 147 x + 343 a . − 4 , − 3 b . − 3 , − 2 c . − 2 , − 1 d . − 1 , 0
For Exercises 41-42, a table of values is given for Y 1 = f x . Determine whether the intermediate value theorem guarantees that the function has a zero on the given interval. Y 1 = 10 x 4 + 21 x 3 − 119 x 2 − 147 x + 343 a . − 4 , − 3 b . − 3 , − 2 c . − 2 , − 1 d . − 1 , 0
Solution Summary: The author analyzes whether the intermediate value theorem guarantees that the given function Y_1=10x4+21
For Exercises 41-42, a table of values is given for
Y
1
=
f
x
.
Determine whether the intermediate value theorem guarantees that the function has a zero on the given interval.
Y
1
=
10
x
4
+
21
x
3
−
119
x
2
−
147
x
+
343
a
.
−
4
,
−
3
b
.
−
3
,
−
2
c
.
−
2
,
−
1
d
.
−
1
,
0
2. Consider the integral √(2x+1)dx
(a) Find the Riemann sum for this integral using
right endpoints and n-4.
(b) Find the Riemann sum for this same integral,
using left endpoints and n=4
5. For the function y-x³-3x²-1, use
derivatives to:
(a) determine the intervals of increase and
decrease.
(b) determine the local (relative) maxima and
minima.
(e) determine the intervals of concavity.
(d) determine the points of inflection.
(e) sketch the graph with the above information
indicated on the graph.
Problem 11 (a) A tank is discharging water through an orifice at a depth of T
meter below the surface of the water whose area is A m². The
following are the values of a for the corresponding values of A:
A 1.257 1.390
x 1.50 1.65
1.520 1.650 1.809 1.962 2.123 2.295 2.462|2.650
1.80 1.95 2.10 2.25 2.40 2.55 2.70
2.85
Using the formula
-3.0
(0.018)T =
dx.
calculate T, the time in seconds for the level of the water to drop
from 3.0 m to 1.5 m above the orifice.
(b) The velocity of a train which starts from rest is given by the fol-
lowing table, the time being reckoned in minutes from the start
and the speed in km/hour:
| † (minutes) |2|4 6 8 10 12
14 16 18 20
v (km/hr) 16 28.8 40 46.4 51.2 32.0 17.6 8 3.2 0
Estimate approximately the total distance ran in 20 minutes.
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