Let
V be the real vector space of functions from (0; 1) to R. Let W be the
set of innitely-di
erentiable functions in
V . Let W+ be the set of positive-
valued functions in
W. We will denote by f0 the derivative of the function
f
.
(a) Prove that
W is a subspace of V .
(b) Let
f and g be vectors inW+. Prove that f and g are linearly independent
if and only if
fg0