Find the linear approximation of $LaTeX: \displaystyle f(x) = \sqrt{x + 9}$ at $LaTeX: \displaystyle a = 0$ and use it to approximate $LaTeX: \displaystyle \sqrt{8.71}$

Using the formula for the linearization $LaTeX: \displaystyle L(x) = f'(a)(x-a)+f(a)$ gives: $LaTeX: f(x) = \sqrt{x + 9} \approx L(x) = \frac{x}{6} + 3$ To approximate $LaTeX: \displaystyle \sqrt{8.71}$ use $LaTeX: \displaystyle x = 8.71-9 = -0.29$ . $LaTeX: \sqrt{8.71} = f(-0.29) \approx L(-0.29) = 2.951667$