Find a basis for the P2 subspace that consists of polynomials p(x) such that p'(5) = 0.
Now if I start with p(x) = ax^2 +bx + c, then derive that, I get
p'(x) = 2ax +b.
then p'(5) = 10a+b.
Where do I go from here to solve this problem?
Thanks for the help.