5. Let f be twice differentiable on (a,b). If g is an antiderivative of f" on (a,b), then g’(x) must equal
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A. f(x) |
B. f’(x) |
C. f"(x) |
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D. f’(x) + C, for some C not necessarily 0 |
E. f"(x) + C, for some C not necessarily 0 |
Solution: The answer is C
By definition, a function g is called an antiderivative of f" on (a,b) if g’(x) = f"(x) for all x in (a,b).