The linearization of the function f(x) = ln(7x) at the point a = 1/7 is derived using the formula L(x) = f(a) + f'(a)(x - a). The calculated value f(1/7) equals 0, while the derivative f'(1/7) is confirmed to be 9.12. Therefore, the correct linearization is L(x) = 0 + 9.12(x - 1/7), which simplifies to L(x) = 9.12x - 1.306. The discussion emphasizes the importance of correctly applying the properties of logarithms, specifically ln(ax) = ln(a) + ln(x), to find the derivative accurately.
PREREQUISITESStudents studying calculus, particularly those focusing on derivatives and linear approximations, as well as educators seeking to enhance their teaching of logarithmic functions and linearization techniques.