f(0)=f(1)=f′(0)=0 Apply Rolles theorem on y=f(x) in x∈[0,1] f(0)=f(1)=0 ⇒f′(α)=0 where α∈(0,1) Now apply Rolles theorem on y=f′(x) in x∈[0,α] f′(0)=f′(α)=0 and f′(x) is continuous and differentiable f′(0)=f′(α)=0 and f′(x) is continuous and differentiable ⇒f"(β)=0 for some ,β∈(0,α)∈(0,1) ⇒f"(x)=0 for some xin∈(0,1)