| OCR Text |
Show 21 is and have if f'=f"=O we A similar set (which derivatives must be zero. zero are called are the are defined as expansion F(u,v) = This is F(r) ar 2 a slice same at 2 Fuu the where + be taken a are local they case, at such: be denoted Fuu, as then are order Taylor Fu=Fv=O. through 1 + 2- 2(v-vo) p\ function the function. univariate parametric polar stationary point. sine (v-vo) = r case r and then we have = r(sin2e Fuu + 2sine case Fuv + cos2e Fvv) sin2e Fuu + 2sin8 cos8 Fuv + cos2e e Fv) derivatives F(uo,vo) v v functions maxima, = + and and Fu second to r 2 u (u-uo) (v-vo)Fuv = (!sin 2 the derivatives second (u-uo) is maximum, stationary points producing the a bivariate local three converting as centered 2 can direction univariate parameter aF 3r a2F 1 have bivariate henceforth of we univariate the consider First 2(u-uO ) + point the types the at to for as these For are will denote types: in As used local a both both stationary point F(uo,vo) coordinates The the at given any three follows. this Through in The three There which have however, looking by point. stationary Fvv. of then f">O defined are where is point. henceforth points. distinguished and will and we stationary points. dF/oV1 Fuv points Locations saddle and f"<O inflection case, we points stationary minima, of and derivative f'=O If two. an this In functions. second f'=O if minimum; the the between distinguish local of sign The zero. Fuu + sine case Fuv Fvv + 1 2"cos2e Fvv) |
