Prove that f(X)=f(X)= x^5 + 2x^3 + 4x -12 has precisely one real root.
Use Intermediate Value Theorem and Rolles's Theorem
Show that f '(x) is positive for all values of x, and that there are values of x for which f(x) is greater than 0 and less than zero, and it's obvious. You'll need to write out a formal proof though.
