Solution:
SOLUTION
Clearly, f(x) must be of the from
f(x)=a0?[xn+(k−x)n]+a1?[xn−1+(k−x)n−1]+...+an−1?[x+(k−x)]+an.?
It may be noted that n must be even for otherwise f(x) will become a polynomial of degree n−1.
Clearly, f′(x) is a polynomial of degree n−1.
