The function

MATHEMATICS · Single correct · IB Diploma Programme · Mathematics: Applications and Interpretation · Number and Algebra · Number and Algebra

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\%

(b)

108\%

(c)

112\%

(d)

12\%