Final answer:
The most general antiderivative of the function f(x) = √7 + √x is √7x + (2/3)x^(3/2) + C.
Step-by-step explanation:
To find the most general antiderivative of the function f(x) = √7 + √x, we can treat the two terms separately:
The antiderivative of √7 is √7x, because when we take the derivative of this function, the √7 term becomes zero. The constant of integration (C) is added to account for any possible constant term in the original function.
The antiderivative of √x is (2/3)x^(3/2), as we add 1 to the exponent (1/2) and divide by the new exponent (3/2). Again, the constant of integration (C) is added.
Combining both antiderivatives, the most general antiderivative of f(x) = √7 + √x is √7x + (2/3)x^(3/2) + C.