Find the average rate of change for f(x) = x2 + 7x + 10 from x = −5 to x = 2.

To find the average rate of change for the function between the two given values of 'x', we need to evaluate the function for each input.

f(-5) = (-5)² + 7(-5) + 10
f(-5) = 0  so the point (-5, 0) is on the parabola

f(2) = (2)² + 7(2) + 10
f(2) = 28  so the point (2, 28) is on the parabola
now we can use the slope formula to find the rate of change between the two points:


So the average rate of change between the values of -5 and 2 for the function is 4... Hope this helps.