Are you sure you have f(x)=5x right? Because the rate of change for a linear function is constant, which makes the assignment a bit moot.
So f(x) = 5^x.
We'll need f(0)=1, f(1)=5, f(2)=25 and f(3)=125.
Rate of change in [0,1]: dy/dx = f(1)-f(0) / (1-0) = 5
Rate of change in [2,3]: dy/dx = f(3)-f(2) / (3-2) = 100
The rate of change in the second section is 20 times higher than the first. This is because f(x) is an exponential function.
