Final answer:
To approximate f(1.1), use the linear approximation formula f(a) + f'(a)(x - a) with known values of f(1) and f'(1), replacing a with 1 and x with 1.1.
Step-by-step explanation:
The student is asking for a linear approximation of a function f at x=1 and then to use this approximation to estimate the value of the function at x=1.1. To find a linear approximation, we generally use the function's value and its derivative at the point of approximation. This is also known as the tangent line approximation or the first-order Taylor expansion. The formula for the linear approximation is f(a) + f'(a)(x - a), where f(a) is the function value at x = a and f'(a) is the derivative at x = a.
I will demonstrate how to perform this calculation using an undefined function f, assuming we have the necessary function value and derivative at x = 1. If f(1) is known as well as f'(1), we just plug these values into the formula along with x = 1.1 to get the approximate value of f(1.1).