All sorted, thank you very much.
It's correct.
Now, f'(1) will give you the slope at x=1. Then you can use the general line formula,
$\displaystyle y=m\cdot x + C$
We know that m = slope = f'(1). And the line must pass the point $\displaystyle (1,f(1))$. Using these, find C. There, you have the equation