MHB Determining the range for a function to be increasing

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The discussion focuses on determining the interval where a function is increasing based on its derivative. It is established that a function increases when its derivative is positive. The function in question decreases from -4 to -2, increases from -2 to 2, and then decreases again from 2 to 4. The correct interval for the function's increase is identified as (-2, 2). Understanding the behavior of the derivative is crucial for determining these intervals.
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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