Question

Let f(x)=x^2+2x+3 . What is the average rate of change for the quadratic function from x=−2 to x = 5?

Answer 1

To find the average rate of change of given function f(x) on a given interval (a,b):

Find f(b)-f(a), b-a, and then divide your result for f(b)-f(a) by your result for b-a:


f(b) - f(a)
------------
b-a

Here your function is f(x) = x^2 - 2x + 3. Substituting b=5 and a=-2,
f(5) = 5^2 -2(5)+3 =? and f(-2) = (-2)^2 - 2(-2) + 3 = ?


Calculate f(5) - [ f(-2) ]
------------------ using your results, above.
5 - [-2]

Your answer to this, if done correctly, is the "average rate of change of the function f(x) = x^2+2x+3 on the interval [-2,5]."