Letf be a real-valued continuous and differentiable function. Let function g be defined by g(x) = f( |x I + 2). A student presents the following proof to show that there exists a real number C E ( 1, 1) such that 3(0) = 0. (I) Sincef is a continuous function, so is g over the interval [ 1, 1]. (II) Sincef is differentiable, so is g over the interval ( 1, 1). (III) It is evident from the definition of g that g( 1) = 3(1). (IV) If the above conditions hold, then by Rolle's theorem, there exists C E (1,1)suchthath(C) = dig?) L = 0. :6 Which statement about this proof is correct? 0 Step (I) does not hold, and hence Rolle's theorem does not apply. 0 Step (II) does not hold, and hence Rolle's theorem does not apply. 0 Step (III) does not hold, and hence Rolle's theorem does not apply. 0 Step (IV) does not hold, and hence the conclusion is false. 0 The proof is completely correct, and the conclusion holds