This was the question assigned to me:
Let $f$ be the function defined by $f(x)=\sqrt x$. Using the line tangent to the graph at $x=9$, what is the approximation of $f(9.3)$?
I know the formula for linear approximation is $$f(x)+f'(x)\Delta x$$ I plugged it in and got: $$3+\frac16(.3)$$ Doing the simple calculation results in $3.05$.
I do not see any problems with how I did this problem. However, I am a beginner and feel I may be missing something. Was this done correctly?