Final answer:
The value of the function f at x=4 given that f(1)=2 and the derivative f'(x)=√x² + 2cos x + 3 cannot be determined without performing the integration of f'(x) from 1 to 4 and adding f(1). The provided information is insufficient to give a numerical answer.
Step-by-step explanation:
The student is asking to find the value of a differentiable function f at a certain point, given the function's value at another point and its derivative. Specifically, the student wants to find f(4) knowing that f(1) = 2 and that the derivative f'(x) is given by the expression √x² + 2cos x + 3.
To solve this, we would integrate the derivative f'(x) from 1 to 4 and add the result to f(1).
However, with the information provided and without the actual integration process, it's not possible to directly provide the value of f(4). The derivatives and functions given in the additional information do not directly relate to the question at hand.