Mathematics

Problem

The function

m(x) = \ln x + e^{-x}

. A student’s calculator, using a default numeric derivative setting, reports

m'(2) \approx -0.043

. The exact derivative is

m'(x) = \frac{1}{x} - e^{-x}

. What is the percent relative error of the calculator’s approximation for

m'(2)

, rounded to the nearest whole percent? a)

41\%

108\%

112\%

12\%