Question

Find the slope of the tangent line and the equation of the tangent line to f(x)=x^2-x at x=3

Answer 1

The slope of the tangent for any x is
f'(x) = 2x-1

So, you want the line

y-f(3) = f'(3) * (x-3)

Answer 2

We weren't allowed to just use derivatives for it we had to do this using limits. That's why I was unsure of this.

Answer 3

I guarantee that your text has this very problem in it. It starts out as the limit of

√(x+h)-√x
------------
h

That's hard to handle, but if you multiply top and bottom by √(x+h)+√x things will drop out nicely when you take the limit.