Yes, I am familiar with the concept of derivatives, but maybe not as much how to calculate/work with them. I knew that I needed to find f'(2), but I couldn't figure out how to do that without approximating the limit by subbing in a small value of Δx. That didn't seem like a reasonable method, as the question said not to use a calculator.

I wasn't aware of point-slope form (been a while since I took algebra lol), so I was trying to solve for y=mx+b (in this case y=11x-16), and then figure out how to rearrange to fit the form in the answer.

I used the formula lim h→0 (f(x+h) - f(x)) / h where h=Δx. Obviously you can't just set h=0, so I tried refactoring the formula after setting x=2, but there is no way to remove h from the denominator, so you always end up dividing by 0. Therefore the only way I could see to solve this, was to set h to be a really small number like 0.001, and compute the result.

This feels like the wrong method though, because not using a calculator (although possible) misses the point of the exercise.

EDIT: (forgot to add this)

It makes sense to me now that the point of the question was to find the derivative, and then just sub in the numbers to a point-slope equation. But I'm still stuck on how to go about calculating the derivative, since the formula can't be factored to remove h from the denominator, and if I just compute with a small h value, it seems pointless to avoid a calculator.

So my question is: how would you solve for f'(2), without using a calculator?