If {{MATH_30}} is not a constant, then it must attain both global extrema in the interval {{MATH_31}}, by the Extreme Value Theorem. One of these two different extrema is attained in the open interval {{MATH_32}} at some point {{MATH_33}}, and the function {{MATH_34}} has a critical point there. Since {{MATH_35}} is differentiable on {{MATH_36}}, it follows that {{MATH_37}}. {{CMD_38}}