Kwa picha zilizo wazi zaidi za yaliyomo kwenye ubao, angalia ukurasa wao wa OCW Scholar kwa kila mhadhara. Huu hapa ndio wa hii. muhadhara: https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/2.-partial-derivatives/part-c-lagrange-multipliers-and-constrained-differentials/session -42-vikwazo-tofauti/####[]