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Let f(x) be a polynomial and g(x) = f'(x) be its derivative. If the degree of (f(x) + f(-x)) is 10, then the degree of (g(x) - g(-x)) is

1. 8
2. 9
3. 10
4. 11

Correct answer: 9

Solution

deg(f(x)+f(-x))=10 means the highest even-degree term of f is x^10. Then g=f' has an x^9 term, and g(x)-g(-x) retains only the odd-degree terms of g; the highest such term is x^9, so the degree is 9.

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