Let . Two tangent lines to are considered: Line : the tangent at . Line : the tangent…
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
Let f(x)=lnx. Two tangent lines to f are considered:
Line L1: the tangent at x=1.
Line L2: the tangent at x=1.2.
The goal is to estimate ln(1.1).
(a) Write an explicit equation for L1 and use it to approximate ln(1.1).
(b) Write an explicit equation for L2 and use it to approximate ln(1.1).
(c) The exact value of ln(1.1) (to six decimal places) is 0.095310. Determine which of the two tangent–line estimates obtained in parts (a) and (b) is closer to this exact value. Support your answer with numerical evidence.