Existence Theorem Assessment Test
10 Questions
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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
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