Final answer:
To find the value of f(7), we add the known value of f(5) and the integral of its derivative from 5 to 7. Using the Fundamental Theorem of Calculus, f(7) is determined to be 32.
Step-by-step explanation:
The student is asking about the value of a function f at a certain point, given the value of the function at another point and the integral of its derivative over a range. Specifically, the student knows that f(5) = 14 and that the integral of f' (f') from 5 to 7 is equal to 18. This question involves understanding the Fundamental Theorem of Calculus which, in this context, tells us that the integral of a derivative f' from a to b gives us the net change in function f from a to b. Hence, if we want to find f(7), we would add this net change to f(5) to get:
f(7) = f(5) + ∫_{5}^{7} f'(x) dx
We substitute the known values to find f(7):
f(7) = 14 + 18 = 32