Question

What is the average rate of change of the function f(x)=(-8)/(-7x+3) from x=-2.5 to x=5.6

Answer 1

The average rate of change of the function f(x) is calculated by finding the function values at x=-2.5 and x=5.6, then determining the difference divided by the change in x over that interval.

Step-by-step explanation:

The average rate of change of a function over an interval can be found by calculating the change in the function values divided by the change in the x values, which is analogous to finding the slope of the secant line connecting the points on the graph of the function corresponding to the interval endpoints.

To find the average rate of change of the function f(x) = (-8)/(-7x + 3) from x=-2.5 to x=5.6, we would first evaluate the function at both x values:

• f(-2.5) = (-8)/(-7(-2.5) + 3) = (-8)/(17.5 + 3) = (-8)/20.5
• f(5.6) = (-8)/(-7(5.6) + 3) = (-8)/(-39.2 + 3) = (-8)/(-36.2)

Then, we find the difference:

• Δy = f(5.6) - f(-2.5)

And the change in x:

• Δx = 5.6 - (-2.5) = 8.1

Finally, we divide:

• Average rate of change = Δy / Δx