Is This Calculation of Average Rate of Change Correct?

In summary, a function change of rate refers to the rate at which the output of a function changes with respect to the input. It can be calculated by finding the slope of the function at a specific point or by taking the derivative of the equation. A positive change of rate indicates an increasing function, while a negative change of rate indicates a decreasing function. A function can also have a constant change of rate, in which case it will appear as a straight line on a graph.
  • #1
Calmwater3000
1
0

Homework Statement


a)find the average rate of change of f from 1 to x:

f(x) - f(1)
----------- , x ≠1
x-1

given f(x) = x^2 - 2 x

Homework Equations


The Attempt at a Solution



RoC(rate of change)=
(x^2 - 2x) - [(1)^2 -2(1)]
-------------------------------
(x-1)
2. By simplifying the equation,
RoC = [(x^2 -2x+1)]/(x-1)


Can anyone check to see if this is right?

Homework Statement


Homework Equations


The Attempt at a Solution

 
Last edited:
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  • #2
You can further simplify the fraction [(x^2 -2x+1)]/(x-1).
 
  • #3
Your solution is correct. The average rate of change of f from 1 to x is given by the formula (f(x) - f(1))/(x-1), where f(x) represents the function x^2 - 2x. By substituting the given function into the formula and simplifying, you have correctly found the average rate of change. Good job!
 

FAQ: Is This Calculation of Average Rate of Change Correct?

What is a function change of rate?

A function change of rate refers to the rate at which the output of a function changes with respect to the input. This can be thought of as the slope or steepness of the function at a specific point. It is a measure of how quickly the output of the function is changing as the input increases or decreases.

How do you calculate the change of rate of a function?

The change of rate of a function can be calculated by finding the slope of the function at a specific point. This can be done by using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the function. Alternatively, if the function is represented by an equation, the change of rate can be found by taking the derivative of the equation.

What does a positive change of rate indicate?

A positive change of rate indicates that the output of the function is increasing as the input increases. This means that the function is getting steeper and steeper as the input increases, and the rate of change is positive. This can be visualized as an upward-sloping line on a graph.

How does a negative change of rate affect a function?

A negative change of rate indicates that the output of the function is decreasing as the input increases. This means that the function is getting flatter and flatter as the input increases, and the rate of change is negative. This can be visualized as a downward-sloping line on a graph.

Can a function have a constant change of rate?

Yes, a function can have a constant change of rate if the slope or steepness of the function remains the same for all values of the input. This means that the rate of change is neither increasing nor decreasing, and the function will appear as a straight line on a graph. An example of a function with a constant change of rate is y = 2x, where the slope is always 2.

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