Divide both sides by to get a linear ODE,
In order for this operation to be valid in the first place, we require that (since that would make undefined, which we don't want to happen). Then we are forcing any solution to the ODE to exist on any of the three intervals, , , or , and either the first or third of these can be chosen as the largest interval.
In case you also need to solve the ODE: Multiply both sides by , so that
Then the left side can be condensed as the derivative of a product, since
and we have
Integrate both sides:
b. the average rate of change of f(x) is less than the average rate of change of g(x).
since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.f(-2) = -3f(1) = 6 . . . estimated from f(x) = (x+2)^2-3, which matches points on the graph (-1,-2) and (0, 1)
so the change in y-value for function f is (6 )) = 9.
the table tells usg(-2) = 1g(1) = 31
so the change in y-value for function g is (31 -1) = 30.
the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).