Precalculus -- determine the rate of change of the function

In summary, the conversation discusses a rate of change problem and the use of the rate of change formula. The solution provided is correct, but it is noted that parentheses should be used in the formula. It is also mentioned that the average rate of change for a curved function will be zero if the starting and ending points are the same.
  • #1
249
3

Homework Statement



BsGt5xN.png


Homework Equations


Rate of change formula: y2-y1/x2-y2

The Attempt at a Solution


If this is a rate of change problem so I use the rate of change formula: y2-y1/x2-y2
and since it's from 2 to 4 I think that would be (2,0) (4,0)
and thus (0-0)/(4-2) = 0/2 = 0

I don't think this is right. What am I doing wrong?
 
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  • #2
Niaboc67 said:

Homework Statement



BsGt5xN.png


Homework Equations


Rate of change formula: y2-y1/x2-y2

The Attempt at a Solution


If this is a rate of change problem so I use the rate of change formula: y2-y1/x2-y2
and since it's from 2 to 4 I think that would be (2,0) (4,0)
and thus (0-0)/(4-2) = 0/2 = 0

I don't think this is right. What am I doing wrong?
Your answer is correct.
Your formula needs parentheses, though. y2 - y1/x2 - x1 means ##y_2 - \frac{y_1}{x_2} - x_1##.
 
  • #3
Yes, your are correct. Since it is a curved function and we are taking the rate of change on that curved interval, it will give us the average rate of change. If you start at zero, and end at zero, on average your rate of change is 0.
 
  • #4
If you start at anything and end at the same thing the averge rate of change is zero, but they have given you a simple example. :D
 

1. What is the definition of rate of change in precalculus?

The rate of change in precalculus refers to the measure of how one quantity changes in relation to another quantity. It is also known as the slope of a function and is represented by the letter "m".

2. How is the rate of change calculated in precalculus?

The rate of change is calculated by finding the slope of a function, which is determined by dividing the change in the output values (y) by the change in the input values (x). This can be represented by the formula: m = (y2 - y1) / (x2 - x1).

3. Can the rate of change be positive or negative?

Yes, the rate of change can be positive or negative depending on the direction of the slope. A positive rate of change indicates an increasing function while a negative rate of change indicates a decreasing function.

4. How is the rate of change used in real-world applications?

The rate of change is used to analyze and predict the behavior of various systems and phenomena in the real world. It is commonly used in physics, economics, and other fields to understand how variables are related and how they change over time.

5. What is the difference between average rate of change and instantaneous rate of change?

The average rate of change refers to the overall change in a function over a specific interval, while the instantaneous rate of change refers to the rate of change at a specific point on a function. It can be thought of as the slope of a tangent line at that point.

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