Consider the natural logarithm function defined on
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
Consider the natural logarithm function f(x)=lnx defined on (0,3). You will approximate a function value near x=1.
(1) Write the equation of the tangent line to the graph of y=f(x) at the point where x=1. Express the line in point–slope form.
(2) Use the tangent line found in part (a) to approximate f(1.2). Give your answer to at least four decimal places.
(3) Determine whether the approximation obtained in part (b) is greater than or less than the actual value of ln(1.2). Provide a clear justification based on properties of f on an appropriate interval.