Using a graph explain why the tangent line approximation is

Question

Consider the function f(x) = .

(a) Find and sketch f(x) and the tangent line approximation to f(x) near x = 4.

(b) Compare the true value of f(4.1) with the value obtained by using the tangent line approximation.

(c) Compare the true and approximate values of f(16).

(d) Using a graph, explain why the tangent line approximation is a good one when x = 4.1 but not when x = 16.