Determining the range for a function to be increasing

In summary, the conversation discusses how the derivative of a function indicates whether the function is increasing or decreasing. It also mentions that the function increases when the derivative is positive and decreases when the derivative is negative. The question being asked is to identify the interval on the x-axis during which the function is increasing, and the correct answer is (-2,2).
  • #1
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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  • #2
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?
 
  • #3
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) ?
 
  • #4
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. :)
 

1. What is the definition of an increasing function?

An increasing function is a function where the output (y-value) increases as the input (x-value) increases. In other words, as x increases, the corresponding y values also increase.

2. How do you determine the range for a function to be increasing?

To determine the range for a function to be increasing, you need to look at the slope of the function. If the slope is positive, then the function is increasing. You can also graph the function and see if it is going up from left to right.

3. Can a function be increasing for some values and decreasing for others?

Yes, it is possible for a function to be increasing for some values and decreasing for others. This happens when the function has a point of inflection, where the slope changes from positive to negative or vice versa.

4. How do you find the range for a piecewise function to be increasing?

To find the range for a piecewise function to be increasing, you need to analyze each piece separately. Look at the slope of each piece and determine if it is positive or negative. If all the pieces have a positive slope, then the function is increasing.

5. What is the difference between a strictly increasing function and a non-decreasing function?

A strictly increasing function is one where the output values must increase with every increase in input values. In other words, the function cannot have any horizontal sections. On the other hand, a non-decreasing function can have horizontal sections, meaning the output values can stay the same for some input values.

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