Help on a quick calc question

let f(x) = e^(x^2). At how many points in the interval [-a.,a] does the instantaneous rate of change of f equal the average rate of change of f?

I know that the instantaneous rate of change is just the first derivative, but what is the average rate of change of f?

thanks!

Basically, you draw a line from the first point to the last point. Think of it this way. Your friend's house is 60 miles away. It takes him an hour to get to you. On average, he went 60miles/hr to get to your house. It doesn't matter if he went 180 mph and then stopped for lunch a mile from your house. You just know that it took him an hour from start to finish.

So look at the start and finish (the range of [-a, a]. Draw a line from the first point to the second. The slope of that line is the average rate of change.

Make sense?