Do you know what "Newton's method" is?
Newton's method, for solving an equation of the form f(x)= 0 is to start with some initial "guess" x_0 and then form a sequence of numbers by x_1= f(x_0)/f'(x_0), x_2= f(x_1)/f'(x_2), ....
Here your function is f(x)= e^(-x/3) - 0.05471*x. What is f'(x)?
The problem asks that you set x_0 to "the endpoint (of [2.5, 2.9]) having the smallest value of |f|".
Okay, what is |f(2.5)|? What is |f(2.9)|?