1. ## tangency

All sorted, thank you very much.

2. Have you learned how to differentiate?

f'(x) gives the slope of the tangent to f(x) at any x point.

3. Thank you. :3

4. It's correct.

Now, f'(1) will give you the slope at x=1. Then you can use the general line formula,

$y=m\cdot x + C$

We know that m = slope = f'(1). And the line must pass the point $(1,f(1))$. Using these, find C. There, you have the equation