Therefore, if the the function {{MATH_207}} is continuous on {{MATH_208}} and differentiable on {{MATH_209}}, then the MVT guarantees that {{CMD_210}} {{CMD_211}} there is a point {{MATH_212}} in {{MATH_213}} where the instantaneous rate of change of {{MATH_214}} is equal to the average rate of change of {{MATH_215}} over the interval {{MATH_216}};