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