What is the average rate of change of fx 2x 1 from x 5 to x 1


Introduction


In mathematics, the average rate of change of a function, f(x), over an interval is the change in f(x), divided by the change in x. It can be thought of as the slope of the tangent line to the graph of f(x) at some point on the interval. In other words, it is a measure of how fast the function is changing at that point.

The average rate of change is useful for many applications. For example, it can be used to find the instantaneous rate of change (or derivative) at a certain point. It can also be used to approximate the function over a small interval.

To calculate the average rate of change, we simply take the difference in f(x) over the interval divided by the difference in x over the interval. That is:

Average Rate of Change = (f(x2) – f(x1)) / (x2 – x1)

where x1 and x2 are points on the interval.

What is the average rate of change of fx 2x 1 from x 5 to x 1?

We can calculate the average rate of change of a function f(x) over a given interval [a, b] by finding the slope of the secant line joining the points (a, f(a)) and (b, f(b)).

In the case of our function f(x) = 2x + 1, we have

f(5) = 2(5) + 1 = 11 and f(1) = 2(1) + 1 = 3

So, the average rate of change of our function from x = 5 to x = 1 is given by:

Average rate of change = (11 – 3)/(5 – 1)
= 8/4
= 2

How to calculate the average rate of change of fx 2x 1 from x 5 to x 1?

To calculate the average rate of change of fx 2x 1 from x 5 to x 1, you would need to find the difference in y values (2x – 1) and divide it by the difference in x values (5 – 1). This would give you an answer of 3/4. You can also use this formula to calculate the average rate of change of any function from one point to another.

Conclusion

From the above calculations, we can see that the average rate of change of fx 2x 1 from x 5 to x 1 is -0.4.


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