4.2.251 AP calculus exam concave ?

In summary, a 4.2.251 AP calculus exam is a standardized test for high school students who have taken AP Calculus BC. The number 4.2.251 refers to the specific section of the curriculum that the exam covers, including topics such as concavity, inflection points, and the second derivative test. The exam is scored on a scale of 1-5 and requires preparation through reviewing concepts, practicing with past exams, and managing time effectively.
  • #1
karush
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ok this one baffled me a little
but isn't $g = e^{-t^2}$and the graph of that has an inflection point at x=1
 

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  • #2
$g’ > 0 \text{ for all } x \in (0,2) \implies g \text{ is increasing}$

$g’’ = e^{-x^2} > 0 \text{ for all } x \in (0,2) \implies g \text{ is concave up}$
 
  • #3

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  • #4
karush said:
how?

how what?
 
  • #5
$\displaystyle g'(x) = \int_0^x e^{-t^2} \, dt$ is the area accumulation function shown in the graph.

\(\displaystyle \color{red}{g'(0.5) = \int_0^{0.5} e^{-t^2} \, dt} < \color{blue}{g'(1) = \int_0^1 e^{-t^2} \, dt} < \color{green}{g'(1.5) = \int_0^{1.5} e^{-t^2} \, dt}\)
 

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FAQ: 4.2.251 AP calculus exam concave ?

1. What is the format of the 4.2.251 AP calculus exam?

The 4.2.251 AP calculus exam follows the standard AP exam format, which includes multiple choice questions, free response questions, and a calculator section. The exam is 3 hours and 15 minutes long and is divided into two sections, with a 10-minute break in between.

2. What topics are covered on the 4.2.251 AP calculus exam?

The 4.2.251 AP calculus exam covers topics such as limits and continuity, derivatives, integrals, and applications of derivatives and integrals. It also includes questions on concavity and related rates, as well as optimization problems.

3. What is the level of difficulty of the 4.2.251 AP calculus exam?

The 4.2.251 AP calculus exam is designed to be challenging and to test students' understanding of advanced calculus concepts. It is considered to be a college-level exam and requires a strong foundation in pre-calculus and basic calculus principles.

4. Is the 4.2.251 AP calculus exam calculator-friendly?

Yes, the 4.2.251 AP calculus exam allows the use of a graphing calculator for certain sections, but there are also sections that must be completed without a calculator. It is important for students to be familiar with their calculator's capabilities and limitations before taking the exam.

5. How can I prepare for the 4.2.251 AP calculus exam?

To prepare for the 4.2.251 AP calculus exam, it is recommended to review all relevant topics covered in the course, practice with past AP exam questions, and take practice exams. It is also important to have a strong understanding of calculus fundamentals and to be familiar with the format and timing of the exam.

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