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Differentiability and Change of Variables
Maxima and Minima
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apply Theorem arbitrarily close b)+hfx(a b)+kfy(a b)fyy(a b+6k b+kt change of variables Chapter consider continuously differentiable course deduce defined differentiable at x=a differentiable functions differential coefficient dv dx example Exercises expression f(a+h fact Find the stationary follows form takes opposite formula function f(x function of x functions of three fx(a fx=p fxx(a fxy(a fy(a fy=q held fixed higher order identically zero IMPLICIT FUNCTIONS Jacobian Lemma mathematical maxima and minima maxima or minima maximum or minimum Mean Value Theorem minima for functions mixed derivatives notation Notice P. J. Hilton P. M. Cohn partial derivatives partial differentiation persistence of inequalities property of gaplessness quadratic form rate of change reader satisfying say that f(x similarly single variable solve stationary points suppose surface takes opposite signs Taylor expansion Taylor's Theorem Theorem 3.1 theorem is proved three variables tion vanishes variations whence write