is average rate of change and average value the same or will you get a different answer for each
this is calculus so it's the mean average. it's using the formula and integrating.
I don't understand your question, but I can assure you that
average rate of change and average value are totally different things. I have no idea what "mean average" means.
I apologize for the confusion. Let me clarify the concepts of average rate of change and average value for you.
Average Rate of Change: In calculus, the average rate of change of a function over a specific interval is the ratio of the change in the function's output (y-values) to the change in the function's input (x-values) over that interval. Mathematically, it is calculated as the slope of a line connecting two points on the function's graph.
To find the average rate of change of a function, you need to select two points on the function's graph, determine the change in y-values between those points, and divide it by the change in x-values. The result represents how much the function is changing on average per unit change in the input variable over the chosen interval.
Average Value: The average value of a function over a specific interval represents the average height of the function's graph over that interval. It is found by integrating the function over the desired interval and dividing the result by the width of the interval.
To find the average value of a function, you need to integrate the function over the given interval and then divide the result by the width of the interval. This gives you the average height of the function over that interval.
In summary, the average rate of change and average value are different concepts. The average rate of change is a measure of how much the function is changing on average per unit change in the input variable, while the average value represents the average height of the function over a given interval.