Let f be a real-yalu ed continuous and differentiable function. Let function g be defined by 9(3) 2 fml + 2). A student presents the following proof to show that there exists a real number 6 E {1, 1) such thathC} = D. {I} Since f is a continuous function, so is 9 over the interval [1, 1]. {II} Since f is differentiable. so is 9 over the interval (1, 1). {III} It is evident from the definition of 9 that g(1) = 9(1). {IV} If the above conditions hold. then by Rolle's theorem. there exists 6 E { 1, 1) such that g' (o) = diam} L_ = ID. 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 I|:|||}I 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. 2 35 Let f be a function 1.rvith the first derivative J\" (I) = :2 for :1: I?" D. It is known that f(1) = 7 and f{5) = 1].. 1What value of a: in the open interval (1, 5} satises the conclusion of the Mean 1|n.I"alue Theorem for f on the closed interval [1, 5]? O 1 0 ME 0 #3 O f does not fulfill the conditions of MRI. and hencer the theorem is not applied