Generalize Exercise 22 as follows: show that, if f .x; y/ ha
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Generalize Exercise 22 as follows: show that, if f .x; y/ has continuous partial derivatives of second order near the po
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Generalize Exercise 22 as follows: show that, if f .x; y/ has continuous partial derivatives of second order near the point .a; b/, then there exists a number satisfying 0< <1 such that, for h and k sufficiently small in absolute value, f .a C h; b C k/ Df .a; b/ C hf1.a; b/ C kf2.a; b/ C h2f11.a C h; b C k/ C 2hkf12.a C h; b C k/ C k2f22.a C h; b C k/: Hence, show that there is a constant K such that for all values of h and k that are sufficiently small in absolute value, ? ? ?f .a C h; b C k/ ? f .a; b/ ? hf1.a; b/ ? kf2.a; b/ ? ? ? K.h2 C k2/
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