Existence Theorem Assessment Test

10 Questions
Existence Theorem Assessment Test

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.

Sample Question

Find the differential dy of the given function. y= 3x 2 - 4

40x dx

12x dx

6x dx  

36x dx

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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