Final answer:
The antiderivative of the function f(x) = 9e^x is F(x) = 9e^x, and it satisfies F(0) = 0.
Step-by-step explanation:
The antiderivative F of the function f(x) = 9e^x is found by applying the power rule of integration. The power rule states that the antiderivative of a function of the form f(x) = ax^n is given by F(x) = (a/n)x^(n+1). In this case, we have f(x) = 9e^x, so applying the power rule, we get F(x) = (9/1)e^x = 9e^x. Since we are given that F(0) = 0, we can substitute x = 0 into the antiderivative to find the constant of integration. So, 0 = 9e^0 = 9, which implies that the constant of integration is 0. Therefore, the antiderivative F(x) = 9e^x satisfies F(0) = 0.