# Finding the average rate of change

I believe there may be some error with my student's teachers homework question:

Let $f(x) = 3x^2 - 2x + 1$. Find the average rate of change between the points $(x,f(2x))$ and $(x,f(x+h)$.

Doing the math I got

$$\frac{-3x^2 + 2x - 6xh + 3h^2 - 2h - 1}{h}$$

All the $h$'s should cancel but they do not. I believe the teacher meant for the point to be $(x,f(x))$. Let me know what you guys think.

• The average rate of change between the points $(x, f(2x))$ and $(x, f(x + h))$ is $$\frac{f(2x) - f(x + h)}{2x - (x + h)} = \frac{f(2x) - f(x + h)}{x - h},$$ so your denominator is wrong. It would be easier to help you if you showed your calculations. – N. F. Taussig Sep 12 '18 at 9:29
• @N.F.Taussig Shouldn't your first denominator be $x-x=0$? I think the problem is riddled with typos. – B. Goddard Sep 12 '18 at 15:26
• @B.Goddard I was not fully awake yet when I read the problem, so I did not notice that the $x$-coordinates did not correspond with the $y$-coordinates. Yes, the problem is riddled with typographical errors. – N. F. Taussig Sep 12 '18 at 15:30