What is the AP calculus exam IVT question?

Click For Summary
SUMMARY

The discussion centers around the Intermediate Value Theorem (IVT) as it pertains to the AP Calculus exam, specifically regarding a function f(x) that transitions from f(2) = 10 to f(4) = 20. Participants emphasize that the continuous nature of f(x) necessitates that it must attain every value between 10 and 20 within the specified interval. The correct answer to the posed question is identified as option A, while other potential answers are deemed invalid due to the lack of specific information about f(x). Visual aids are suggested to enhance understanding of the function's behavior.

PREREQUISITES
  • Understanding of the Intermediate Value Theorem (IVT)
  • Knowledge of continuous functions
  • Familiarity with function notation and behavior
  • Basic graphing skills for visual representation of functions
NEXT STEPS
  • Study the implications of the Intermediate Value Theorem in calculus
  • Explore examples of continuous functions and their properties
  • Practice sketching functions that meet specific criteria
  • Review past AP Calculus exam questions related to IVT
USEFUL FOR

Students preparing for the AP Calculus exam, educators teaching calculus concepts, and anyone seeking to deepen their understanding of the Intermediate Value Theorem and its applications.

karush
Gold Member
MHB
Messages
3,240
Reaction score
5
View attachment 9602
Ok I thot I posted this before but after a major hunt no find

Was ? With these options since if f(x) Is a curve going below the x-axis Is possible and () vs []

If this is a duplicate post
What is the link.. I normally bookmark these
Mahalo ahead
 

Attachments

  • 2020_03_14_10.47.05_edit.jpg
    2020_03_14_10.47.05_edit.jpg
    22.1 KB · Views: 176
Physics news on Phys.org
karush said:
Ok I thot I posted this before but after a major hunt no find

Was ? With these options since if f(x) Is a curve going below the x-axis Is possible and () vs []

If this is a duplicate post
What is the link.. I normally bookmark these
Mahalo ahead
Since we aren't given any real information about f(x) we need to be general. It's possible that f(x) can be just about anywhere is this interval. But note that the (continuous) function has to go from f(2) = 10 to f(4) = 20. So it has somehow get to 20 from 10. At some point the function has to hit every value between 10 and 20. (See the image for a visual.)

-Dan
View attachment 9603
 

Attachments

  • f(x).jpg
    f(x).jpg
    9.4 KB · Views: 150
Would not your free hand line not be a function failing a vertical line test
 
karush said:
Would not your free hand line not be a function failing a vertical line test
I'm just saying that f(x) can be anything so I had fun sketching it.

-Dan
 
Ok I'll post on the frig door.. just for reactions 🕶 Well the book said the answer was A
Which fits your observation

But not sure why the others are no no's
 
karush said:
Ok I'll post on the frig door.. just for reactions 🕶 Well the book said the answer was A
Which fits your observation

But not sure why the others are no no's
All of the other answers could be true but since f(x) is not given we could make the function do some or all of these possibilities, as well as others. A good exercise is to find an f(x) that have these properties.

-Dan
 

Similar threads

MHB 2.1.314 AP Calculus Exam a particle moves along the x-axis......
  • · Replies 1 ·
Replies
1
Views
2K
MHB 1.4.293 AP Calculus Exam a(t) and v(t) t=8
  • · Replies 6 ·
Replies
6
Views
2K
MHB 9.2.2 AP Calculus Exam Slope Fields
  • · Replies 4 ·
Replies
4
Views
2K
MHB What Is the Total Distance Traveled by the Particle from t = 0 to t = 3?
  • · Replies 4 ·
Replies
4
Views
2K
MHB 3.4.238 AP calculus exam Limits with ln
  • · Replies 1 ·
Replies
1
Views
2K
MHB 4.2.204 AP calculus practice question
  • · Replies 6 ·
Replies
6
Views
2K
MHB 1.4.203 AP calculus practice question on Limits
  • · Replies 1 ·
Replies
1
Views
2K
MHB 4.2.236 AP calculus Exam integral with u substitution
  • · Replies 4 ·
Replies
4
Views
2K
MHB 4.1.237 AP calculus exam find area
  • · Replies 4 ·
Replies
4
Views
2K
MHB What Does the Intermediate Value Theorem Guarantee for a Continuous Function?
  • · Replies 1 ·
Replies
1
Views
2K