Because {{MATH_31}} is {{CMD_32}}{{CMD_33}}continuous{{CMD_34}}{{CMD_35}}differentiable{{CMD_36}}{{CMD_37}} on the interval {{MATH_38}} and {{MATH_39}} is {{CMD_40}}{{CMD_41}}continuous{{CMD_42}}{{CMD_43}}differentiable{{CMD_44}}{{CMD_45}} on the interval {{MATH_46}}, {{MATH_47}} satisfies the conditions of the Mean Value Theorem.