Whether the intermediate value theorem guarantees or not that the function Y 1 = 21 x 4 + 46 x 3 − 238 x 2 − 506 x + 77 has a zero in the interval [ − 4 , − 3 ] . The table is as follows: x Y 1 − 4 725 − 3 − 88 − 2 105 − 1 320 0 77 1 − 600 2 − 1183 3 − 640 4 2565 5 10472 6 25625
Whether the intermediate value theorem guarantees or not that the function Y 1 = 21 x 4 + 46 x 3 − 238 x 2 − 506 x + 77 has a zero in the interval [ − 4 , − 3 ] . The table is as follows: x Y 1 − 4 725 − 3 − 88 − 2 105 − 1 320 0 77 1 − 600 2 − 1183 3 − 640 4 2565 5 10472 6 25625
Solution Summary: The author evaluates whether the intermediate value theorem guarantees or not that the function Y_1=21x4+46
Whether the intermediate value theorem guarantees or not that the function Y1=21x4+46x3−238x2−506x+77 has a zero in the interval [−4,−3]. The table is as follows:
x
Y1
−4
725
−3
−88
−2
105
−1
320
0
77
1
−600
2
−1183
3
−640
4
2565
5
10472
6
25625
(b)
To determine
Whether the intermediate value theorem guarantees or not that the function Y1=21x4+46x3−238x2−506x+77 has a zero in the interval [−3,−2]. The table is as follows:
x
Y1
−4
725
−3
−88
−2
105
−1
320
0
77
1
−600
2
−1183
3
−640
4
2565
5
10472
6
25625
(c)
To determine
Whether the intermediate value theorem guarantees or not that the function Y1=21x4+46x3−238x2−506x+77 has a zero in the interval [−2,−1]. The table is as follows:
x
Y1
−4
725
−3
−88
−2
105
−1
320
0
77
1
−600
2
−1183
3
−640
4
2565
5
10472
6
25625
(d)
To determine
Whether the intermediate value theorem guarantees or not that the function Y1=21x4+46x3−238x2−506x+77 has a zero in the interval [−1,0]. The table is as follows:
6) A farmer has 60 acres on which to plant oats or corn. Each acre of oats requires 100 lbs of fertilizer and 1 hour
of labor. Each acre of corn requires 50 lbs of fertilizer and 2 hours of labor. The farmer has 5000 lbs of
fertilizer and 100 hours available for labor. If the profit is $60 from each acre of oats and $100 from each acre
of corn, what planting combination will produce the greatest total profit?
a) Fill in the following chart to help organize the information given in the problem:
Oats
Labor
Fertilizer
Land
Profit
b) Write down the question of interest.
Corn
Available
c) Define variables to answer the question of interest. Call these x and y.
d) Write the objective function to answer the question of interest.
e) List any constraints given in the problem.
I need help with number 5.
3) Use the following system of linear inequalities graphed below to answer the questions.
a) Use the graph to write the symbolic form of the system
of linear inequalities.
b) Is (-4,2) a solution to the system? Explain.
5
-7
-5
-3
-2
0
2
3
4
$
6
-2
-6
-7
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