Question

Find the most general antiderivative of the function f(x) = 4x⁹. Check your answer by differentiation. Use c for the constant of the antiderivative.

Answer 1

The most general antiderivative of the function f(x) = 4x⁹ is F(x) = (1/10)x¹⁰ + c, which can be checked by differentiating it.

Step-by-step explanation:

The most general antiderivative of the function f(x) = 4x⁹ is F(x) = (1/10)x¹⁰ + c, where c is the constant of the antiderivative.

To check this answer, we can differentiate F(x) using the power rule of differentiation. The derivative of F(x) is f(x) = 4x⁹, which confirms that F(x) is indeed the antiderivative of f(x).