Consider the following functions:
f(x) = cos(2x)
f'(x) = 1
f''(x) = cos^2(x) + (x + (xy + (x^6)
Solve for C, C^2, and cg so that g(x) = 0 on the interval (-∞, ∞). If a nontrivial solution exists, state it. (If only the trivial solution exists, enter the trivial solution {0, 0, 0}.)
Determine whether f, f', f'' are linearly independent on the interval (-∞, ∞).