The second version of this theorem states that the integral of a product of two functions is equal to an output value of one of the functions multiplied by the integral of the other function.
The second version of this theorem states that the integral of a product of two functions is equal to an output value of one of the functions multiplied by the integral of the other function. The version of this theorem named after Cauchy (koh-SHEE) can be used to prove L'Hôpital's (lo-pee-TAHL's) rule. A special case of this theorem, proven by the continuity property and extreme value theorem, is named Rolle's (ROHL's) theorem. If you travel a distance of sixty miles in one hour, this theorem guarantees that at some point in time you traveled sixty miles per hour. Name this theorem that, for a function continuous on a closed interval and differentiable on that interval's interior, guarantees the existence of a point whose tangent line has the same slope as the average slope of the interval.
The second version of this theorem states that the integral of a product of two functions is equal to an output value of one of the functions multiplied by the integral of the other function.
{mean value theorem} [accept {MVT}]