Let f (x) be a function that f ′(x) = x2 + 2x + 2. Suppose that f (−1) = −1. What is f (2)?A. -1B. 1C. 11D. 17E. -17
Question
Solution 1
To find f(2), we first need to find the antiderivative of f'(x) = x^2 + 2x + 2.
The antiderivative of x^2 is (1/3)x^3, the antiderivative of 2x is x^2, and the antiderivative of 2 is 2x. So, the antiderivative of f'(x) is (1/3)x^3 + x^2 + 2x + C, where C is the constant of integration.
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