Existence Theorem Assessment Test
10 Questions
| Total Attempts: 131
Existence theorems are mathematical theorems with a statement that begins with 'there exist(s). . '. It is a theorem with a prenex normal form involving the existential quantifier. Take this test to find out more.
Questions and Answers
- 1.
Find the differential dy of the given function. y= 3x 2 - 4- A.
40x dx
- B.
12x dx
- C.
6x dx
- D.
36x dx
- 2.
Find the limit. lim(4 + 3/x) x->∞
- A.
1
- B.
2
- C.
3
- D.
4
- 3.
The Rolle's Theorem is named after who?
- A.
Michel Rolle
- B.
Janet Rolle
- C.
Albert Rolle
- D.
Pierce Rolle
- 4.
Find any critical numbers of the function. f(x)= x 3 - 3x 2
- A.
X=1 , x=2
- B.
X=0 , x =3
- C.
X=1 , x=3
- D.
X=0 , x=2
- 5.
If there is an open interval containing c on which f(c) is a maximun, then f(c) is called...
- A.
Absolute minimum
- B.
Relative maximum
- C.
Absolute maximum
- D.
Relative minimum
- 6.
If f is continuous on a closed interval [a,b], then f has both a minimum and a maximum on the interval.
- A.
The mean value theorem
- B.
Pythagoraean theorem
- C.
Binomial theorem
- D.
The extreme value theorem
- 7.
What is the average rate of change of the function below over the indicated interval? f(x) = x2 - 3x - 28, [-4,7]
- A.
11
- B.
66
- C.
6
- D.
0
- 8.
What is the average rate of change of the function below over the indicated interval? f(x) = 12√(x), [1,16]?
- A.
12/5
- B.
0
- C.
1
- D.
24
- 9.
What is x-value at which the function below has the same slope as the average rate of change over the indicated interval? f(x) = 12√(x), [1,16]?
- A.
24
- B.
18.78
- C.
6.25
- D.
7.35
- 10.
The graph of f is concave upward or downward on I if f ' is increasing on the interval...
- A.
Concave upwards
- B.
Convex upwards
- C.
Concave downwards
- D.
Convex downwards
![If f is continuous on a closed interval [a,b], then f has both a minimum and a maximum on the interval. - ProProfs](https://media.proprofs.com/images/QM/user_images/2170919/1514457213.png "If f is continuous on a closed interval [a,b], then f has both a minimum and a maximum on the interval.")
![What is the average rate of change of the function below over the indicated interval? f(x) = x2 - 3x - 28, [-4,7] - ProProfs](https://media.proprofs.com/images/QM/user_images/2170919/1514457445.JPG "What is the average rate of change of the function below over the indicated interval? f(x) = x2 - 3x - 28, [-4,7]")
![What is the average rate of change of the function below over the indicated interval? f(x) = 12√(x), [1,16]? - ProProfs](https://media.proprofs.com/images/QM/user_images/2170919/1514457552.JPG "What is the average rate of change of the function below over the indicated interval? f(x) = 12√(x), [1,16]?")
![What is x-value at which the function below has the same slope as the average rate of change over the indicated interval? f(x) = 12√(x), [1,16]?
- ProProfs](https://media.proprofs.com/images/QM/user_images/2170919/1514458315.png "What is x-value at which the function below has the same slope as the average rate of change over the indicated interval? f(x) = 12√(x), [1,16]?")
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