Need help with this question pleasee!!! Can someone help me with the proof of th

Need help with this question pleasee!!!
Can someone help me with the proof of this question a and b pleasee
Problem 7. Suppose f is continuous on [0, 1] and differentiable on (0, 1).( a) Prove that if {In} is a Cauchy sequence in [0, 1] then {f (x’n) } is a Cauchy sequence.(b) If f(0) = 0 and f(1) = 2, prove that there is a point x E (0, 1) with3f (x)2 – 4f (x) = -1.(c) If f(0) = 0 and f(1) = ;, prove that there is a point c E (0, 1) with6f (c)f’ (c) – 4f'(c) = -5