differential equation: Show that if f and f' are continuous on a ≤ x ≤ b then f and f' are linearly independent on a ≤ x ≤ b

Show that if f and f' are continuous on a ≤ x ≤ b and f(x) is not zero for all x on a ≤ x ≤ b,
then f and xf are linearly independent on a ≤ x ≤ b.