GATE 2016 CS (CS2) – Question 12
Let f(x) be a polynomial and $g(x)=f\prime(x)$. If f(x)+f(−x) has degree 10, find the degree of g(x)−g(−x).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 9.0 to 9.0
Explanation
The sum retains twice the even-degree terms of f, with leading degree ten. Their derivatives are precisely the odd-degree terms retained in g(x)−g(−x). Differentiating the nonzero degree-ten term yields a nonzero degree-nine term. Thus the answer is 9.