What is the AP calculus exam IVT question?

In summary, the book says that f(x) can be anything so the author sketched it as a freehand line. However, the other answers are also possible and the author didn't explain why they are no no's.
  • #1
karush
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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
 

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  • #2
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
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  • #3
Would not your free hand line not be a function failing a vertical line test
 
  • #4
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
 
  • #5
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
 
  • #6
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
 
  • #7

1. What is the 1.8.3 AP calculus exam?

The 1.8.3 AP calculus exam is a standardized test administered by the College Board to assess a student's understanding of calculus concepts at the AP level. It covers topics such as limits, derivatives, integrals, and the fundamental theorem of calculus.

2. What is the IVT in calculus?

The IVT, or Intermediate Value Theorem, is a fundamental theorem in calculus that states that if a function is continuous on a closed interval, then it must take on every value between the minimum and maximum values of the function on that interval.

3. How is the IVT used in the 1.8.3 AP calculus exam?

The IVT is often used in calculus problems to prove the existence of a solution or to show that a function has a root or zero within a certain interval. It may also be used to find approximate solutions to equations or to show that a function is continuous on a given interval.

4. What is the difference between the IVT and the EVT?

The EVT, or Extreme Value Theorem, is another fundamental theorem in calculus that states that if a function is continuous on a closed interval, then it must have both a maximum and minimum value on that interval. The main difference between the IVT and EVT is that the IVT deals with all values between the minimum and maximum, while the EVT focuses on the extreme values themselves.

5. How can I prepare for the 1.8.3 AP calculus exam?

To prepare for the 1.8.3 AP calculus exam, it is important to review and understand all of the key concepts covered in the course. Practice problems and past exams can also be helpful in familiarizing yourself with the types of questions that may be asked. Additionally, seeking help from a teacher or tutor can provide valuable guidance and support in preparing for the exam.

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