a) Use the intermediate value theorem to show that the function f(x)=x-4x+1 has a root on the interval [0,1]. b) Can you use IVT to prove the existence of the roots for: f(x)=2x+3x+1 on [1,2]? Justify your answer. c) Can you use IVT to prove the existence of the roots for: X f(x)=- on [1,4]? Justify your answer. x-3