If f'(x) = x^2 and f(0) = 4, what is f(2)?

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Multiple Choice

If f'(x) = x^2 and f(0) = 4, what is f(2)?

Explanation:
Finding f(2) involves constructing the antiderivative of f' and using the given point to determine the constant of integration. Since f'(x) = x^2, an antiderivative is f(x) = x^3/3 + C. The condition f(0) = 4 gives C = 4. Then f(2) = (2^3)/3 + 4 = 8/3 + 4 = 20/3.

Finding f(2) involves constructing the antiderivative of f' and using the given point to determine the constant of integration. Since f'(x) = x^2, an antiderivative is f(x) = x^3/3 + C. The condition f(0) = 4 gives C = 4. Then f(2) = (2^3)/3 + 4 = 8/3 + 4 = 20/3.

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