# 4.1.286 AP Calculus Exam .... table of f(t).

• MHB
• karush
In summary, the conversation discusses the conditions for a function with a positive slope and how it could be represented in tables. There is also mention of an integral statement and the possible solutions for the function. Ultimately, the group agrees that option D is the most likely solution.
karush
Gold Member
MHB
View attachment 9426
ok these always baffle me because f(t) is not known. however if $f'(t)>0$ then that means the slope is aways positive which could be just a line. but could not picture this to work in the tables.
Im sure the answer can be found quickly online but I don't learn by copy and paste. d was attractive but where would the slope be?
so any sugest..

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check that integral statement ... you sure the upper limit is t and that it's not an inequality?

I'm thinking maybe it should be something like $\displaystyle \int_4^x f(t) \, dt > 0$

skeeter said:
check that integral statement ... you sure the upper limit is t and that it's not an inequality?

I'm thinking maybe it should be something like $\displaystyle \int_4^x f(t) \, dt > 0$
I'm guessing it should be $$\displaystyle \int_4^7 f(t) \, dt = 0$$.

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karush said:
here is the original
yeah probably 7 clipped

Well, you can throw out (C) and (D) since $f'(t)$ is not > 0 for all $t$ in the interval

You can throw out (E) since $f(t) \ge 0$ for all $t$ in the interval

You can throw out (A) since $f(t) \le 0$ for all $t$ in the interval

Since the problem only asks for a possible function, "D" leaps out immediately!

## 1. What is the purpose of the "4.1.286 AP Calculus Exam .... table of f(t)"?

The purpose of this table is to provide a comprehensive overview of the function f(t) for the 4.1.286 AP Calculus Exam. It includes values of f(t) at different points, as well as information about the function's behavior and characteristics.

## 2. How is the table of f(t) organized?

The table is typically organized in a grid format, with columns for the values of t and f(t), and additional columns for any other relevant information, such as the slope or concavity of the function at each point.

## 3. What does the table of f(t) tell us about the function?

The table provides a visual representation of the function f(t) and allows us to analyze its behavior and characteristics at different points. It can help us identify patterns and make predictions about the function's behavior in other parts of the graph.

## 4. How can the table of f(t) be used to solve calculus problems?

The table can be used to find the values of f(t) at specific points, calculate the slope or concavity of the function, and determine the intervals where the function is increasing or decreasing. This information can be used to solve various calculus problems, such as finding the maximum or minimum value of the function or finding the area under the curve.

## 5. Is the table of f(t) the only resource needed for the AP Calculus Exam?

No, the table of f(t) is just one of many resources that may be provided for the exam. It is important to also have a solid understanding of calculus concepts and techniques, as well as the ability to apply them to solve problems.

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