# Which Interval Shows f' Always Increasing?

• MHB
• karush
In summary, the conversation discusses how to solve a problem using observation and determining the slope of a function as it moves in the positive direction. The only interval where the slope is always increasing is at point e. The conversation also clarifies that e is a point, not an interval, and that at point e the slope is increasing.
karush
Gold Member
MHB
View attachment 9411image due to macros in overleaf

well apparently all we can do is solve this by observation
which would be the slope as x moves in the positive direction
e appears to be the only interval where the slope is always increasing

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karush said:
image due to macros in overleaf

well apparently all we can do is solve this by observation
which would be the slope as x moves in the positive direction
e appears to be the only interval where the slope is always increasing

You have not correctly understood or interpreted the question. e is a point, not an interval.

"always increase" doesn't mean anything for a point. Either it's increasing at that point or it isn't.

Ok good point

Well at point e the slope is increasing

At point a the function is decreasing so f' is negative, not positive. At point b there is a cusp so f' does not even exist there. At point c the function is increasing so f' is positive but the graph is "flattening" so f' is decreasing, not increasing. At point d the function is decreasing so f' is negative, not positive. At point e the function is increasing so f' is positive and the graph is getting steeper so f' is increasing. Yes, e is the correct answer.

## 1. What does "3.3.300 AP Calculus f' interval" refer to?

"3.3.300 AP Calculus f' interval" refers to a specific topic in AP Calculus, specifically the interval of a function's derivative.

## 2. Why is the "3.3.300 AP Calculus f' interval" important?

The "3.3.300 AP Calculus f' interval" is important because it helps us understand the behavior of a function and its rate of change. It also allows us to determine critical points and intervals of increasing or decreasing values.

## 3. How is the "3.3.300 AP Calculus f' interval" calculated?

The "3.3.300 AP Calculus f' interval" is calculated by finding the derivative of a function and determining the points where the derivative is equal to zero or undefined. These points, along with the endpoints of the given interval, make up the "3.3.300 AP Calculus f' interval".

## 4. What is the significance of the "3.3.300 AP Calculus f' interval" in real-world applications?

In real-world applications, the "3.3.300 AP Calculus f' interval" can help us analyze the behavior of a function and make predictions about its future values. This is especially useful in fields such as economics, physics, and engineering.

## 5. Are there any tips for effectively understanding the "3.3.300 AP Calculus f' interval"?

To effectively understand the "3.3.300 AP Calculus f' interval", it is important to have a solid understanding of derivatives and their properties. It may also be helpful to practice identifying critical points and intervals on graphs and working through example problems.

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