A-ball-lies-on-the-function-z-xy-at-the-point-1-2-2-Find-the-point-in-the-xy-plane-where-the-ball-will-touch-it-Calculus-2-problem-

Question Number 200929 by Akira181 last updated on 26/Nov/23

$$\mathrm{A}\:\mathrm{ball}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{function}\:{z}={xy}\:\mathrm{at} \\ $$$$\mathrm{the}\:\mathrm{point}\:\left(\mathrm{1},\mathrm{2},\mathrm{2}\right).\:\mathrm{Find}\:\mathrm{the}\:\mathrm{point}\:\mathrm{in} \\ $$$$\mathrm{the}\:{xy}−\mathrm{plane}\:\mathrm{where}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{will} \\ $$$$\mathrm{touch}\:\mathrm{it}. \\ $$$$\mathrm{Calculus}\:\mathrm{2}\:\mathrm{problem}. \\ $$

Commented by Akira181 last updated on 26/Nov/23

$$\mathrm{The}\:\mathrm{ball}\:\mathrm{always}\:\mathrm{goes}\:\mathrm{down}\:\mathrm{in}\:\mathrm{the}\: \\ $$$$\mathrm{direction}\:\mathrm{of}\:\mathrm{the}\:\mathrm{steepest}\:\mathrm{slope}. \\ $$

Commented by mr W last updated on 02/Dec/23

$${my}\:{answer}\:{see}\:{Q}\mathrm{201214}.\:{please} \\ $$$${check}\:{if}\:{it}\:{is}\:{correct}. \\ $$

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