Determine if the function F is the general antiderivative of the function f. F(x) = 5x + C; f(x) = 5

Question

Determine if the function F is the general antiderivative of the function f. F(x) = 5x + C;  f(x) = 5

Quizplus · Accepted Answer

To check if F(x) is the general antiderivative of f(x), we need to take the derivative of F(x) and see if it equals f(x). 
Taking the derivative of F(x) with respect to x, we get:
F'(x) = 5
Since f(x) is given as 5, we see that F'(x) = f(x). 
Thus, F(x) is a valid antiderivative of f(x), along with any other function obtained by adding a constant to F(x). This is because the derivative of a constant is 0, so adding a constant to F(x) would not change its derivative, and hence it would still be a valid antiderivative of f(x).

Determine If the Function F Is the General Antiderivative of the Function