Am I Doing a Linear Approximation on $\sqrt x$ Correctly?

Question

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?

Answer 1

This looks correct. In fact, if you use a calculator to compute $\sqrt{9.3},$ you’ll see that your linear approximation is very good.