4.2 Class Notes - April 19 Prelim 3 on Tuesday April 24...

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April 19Prelim 3 on Tuesday April 24 covers7.4 Definite integrals8.2 Volumes, 8.4 Improper Integrals8.1 Integration by partsCh. 11. Probability distributions9.2 Partial derivativesi.e., the material from HWK 7,8,9Formula and review sheets on BlackboardPartial Derivatives22222222( ,)47340230 070322 2 3f x yxyxxyyfxyxfxyyffxyffy xx y=++=++=++== −= −=∂ ∂∂ ∂Meaning of partial erivatives222rate of change of when is fixedsecond derivative w.r.t. when is fixedrate of change of when changesrate of change of when y changesfxyxfxyxfxxffy xx====∂ ∂Partial Derivatives22222222( ,)473( ,2)10222 (1,)5442at 1,2 0,0 curve is flat2 2 neither min nor maxf x yxyxxyyff xxxxxffyyyyyffxyxyffxy=++=+= −+=+======= −f(x,y) = 4x + 7y + x2– 3xy – y2saddle surface

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