MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
Let f(x)=x for x>0. The point (9,3) lies on the graph of f.
(a) Write the equation of the tangent line to the graph of f at x=9. Express the equation in point–slope form.
(b) Use this tangent line to approximate f(9.4). Show all work leading to your approximation.
(c) Decide whether your approximation in part (b) is an underestimate or an overestimate of the exact value of f(9.4). Justify your conclusion analytically by referencing appropriate properties of f on an interval that includes x=9. No numerical evaluation of 9.4 is required.