Chapter 3, Problem 104RE

Consider the function $f(x)=\sqrt{x}.$

1. (a) Find and sketch f(x) and the tangent line approximation to f(x) near x = 4.
2. (b) Compare the true value of f(4.1) with the value obtained by using the tangent line approximation.
3. (c) Compare the true and approximate values of f(16).
4. (d) Using a graph, explain why the tangent line approximation is a good one when x = 4.1 but not when x = 16.