Consider the function #f(x) = sqrt(1-x^2)# on the interval [0, -1], how do you find the average or mean slope of the function on this interval?
2 Answers
The slope of a function
The average value of a function
We want to find the average slope of the function
Its slope at any given point is
By the Fundamental Theorem of Calculus, we know that integration and differentiation are inverse operations. Thus, we have the above expression equal to
We can verify this via a graph:
graph{sqrt(1-x^2) [-3,3,-1.5,1.5]}
By inspection, it seems that the average slope of
The slope is the same as the rate of change.
Explanation:
Note that the "interval
I will assume that you mean
The slope is the same as the rate of change.
So the average slope on
If the intended interval is