Determining the range for a function to be increasing

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Discussion Overview

The discussion revolves around determining the range for a function to be increasing, focusing on the use of derivatives to identify intervals of increase and decrease. Participants explore the behavior of a specific function over the interval from -4 to +4.

Discussion Character

  • Mathematical reasoning, Conceptual clarification

Main Points Raised

  • Some participants propose that the derivative indicates whether a function is increasing or decreasing, with positive derivatives signifying increase and negative derivatives signifying decrease.
  • One participant observes that the function appears to be increasing from -2 to 2, suggesting this interval as the answer.
  • Another participant confirms the proposed interval of increase as correct.

Areas of Agreement / Disagreement

There is a partial agreement on the interval during which the function is increasing, specifically from -2 to 2, but the discussion does not clarify if this is universally accepted or if other interpretations exist.

Contextual Notes

The discussion does not address potential assumptions about the function's behavior outside the specified interval or the nature of the function itself.

swag312
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Hi, it would be really nice if someone could give me a correct answer with a little explanation to this question. Thanks.
 

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Re: Math help

swag312 said:
Hi, it would be really nice if someone could give me a correct answer with a little explanation to this question. Thanks.
Hi swag312, and welcome to MHB.

One of the things that the derivative tells you is whether the function is increasing or decreasing. The function increases when the derivative is positive, and decreases when the derivative is negative.

As $x$ goes from $-4$ to $+4$, you can see from the graph that the function starts by decreasing, then it increases, and finally it decreases again. So what is the interval along the $x$-axis during which the function is increasing?
 
Re: Math help

Opalg said:
Hi swag312, and welcome to MHB.

One of the things that the derivative tells you is whether the function is increasing or decreasing. The function increases when the derivative is positive, and decreases when the derivative is negative.

As $x$ goes from $-4$ to $+4$, you can see from the graph that the function starts by decreasing, then it increases, and finally it decreases again. So what is the interval along the $x$-axis during which the function is increasing?

Ahh, so it looks like it's increasing from -2 to 2 in which case the answer is A ? (-2;2) ?
 
Re: Math help

swag312 said:
Ahh, so it looks like it's increasing from -2 to 2 in which case the answer is A ? (-2;2) ?
Yes. :)
 

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