∵f(1/2)=f(0)+f'(0)/2+f''(θ)/8=f(1)-f'(1)/2+f''(φ)/8
∴|f''(θ)-f''(φ)|=8
∵|f''(θ)-f''(φ)|≤|f''(θ)|+|f''(φ)|≤2max|f''(x)|
∴max|f''(x)|≥4
∴存在ξ∈(0,1),使|f''(ξ)|≥4