Suppose f is a continuous function on R satisfying: lim f(x) (when x goes to negative infinity) = 0 = lim f(x) (when x goes to positive infinity).

Suppose f is a continuous function on R satisfying: lim f(x) (when x goes to negative infinity) = 0 = lim f(x) (when x goes to positive infinity).Prove that f is bounded and attains either a maximum value or a minimum value on R.