Question

For which function is the average rate of change over the interval 1 < x < 5 greater than the average rate of change over the same interval for the function g(x)

Answer 1

Answer: x=2 and x=6

Explanation:

Answer 2

We do not have the function g(x), but this can be solved in a trivial way.

The average rate of change in a interval is the slope over that interval, so the average rate of change of g(x) in the interval 1 < x < 5 is

p = (g(x2) - g(x1))/(x2 - x1) where x2 > x1

p = (g(5) - g(1))/(5 - 1) = (g(5) - g(1))/4

Now, suppose that i have the new equation h(x) = g(x) + x

the rate of change of this function, the average rate of change in the interval will be:

p' = (h(5) - h(1))/(5 - 1) = (g(5) + 5 - g(1) - 1)/4 = (g(5) - g(1))/4 + 4/4 = p +1

so p' > p

and the average rate of change of h(x) is bigger than the one of g(x) in the interval 1< x < 5