Exam 7: Ingredients of Multivariable Change: Models, Graphs, Rates

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The contour graph The contour graph   and its associated three-dimensional graph are given below. Determine (if possible) if the change in   will be greater when   shifts to   or when   shifts to      and its associated three-dimensional graph are given below. Determine (if possible) if the change in The contour graph   and its associated three-dimensional graph are given below. Determine (if possible) if the change in   will be greater when   shifts to   or when   shifts to      will be greater when The contour graph   and its associated three-dimensional graph are given below. Determine (if possible) if the change in   will be greater when   shifts to   or when   shifts to      shifts to The contour graph   and its associated three-dimensional graph are given below. Determine (if possible) if the change in   will be greater when   shifts to   or when   shifts to      or when The contour graph   and its associated three-dimensional graph are given below. Determine (if possible) if the change in   will be greater when   shifts to   or when   shifts to      shifts to The contour graph   and its associated three-dimensional graph are given below. Determine (if possible) if the change in   will be greater when   shifts to   or when   shifts to      The contour graph   and its associated three-dimensional graph are given below. Determine (if possible) if the change in   will be greater when   shifts to   or when   shifts to      The contour graph   and its associated three-dimensional graph are given below. Determine (if possible) if the change in   will be greater when   shifts to   or when   shifts to

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The contour graph The contour graph   and its associated three-dimensional graph are given below. At   will   decrease more quickly as x decreases or as y decreases? Justify your answer.    and its associated three-dimensional graph are given below. At The contour graph   and its associated three-dimensional graph are given below. At   will   decrease more quickly as x decreases or as y decreases? Justify your answer.    will The contour graph   and its associated three-dimensional graph are given below. At   will   decrease more quickly as x decreases or as y decreases? Justify your answer.    decrease more quickly as x decreases or as y decreases? Justify your answer. The contour graph   and its associated three-dimensional graph are given below. At   will   decrease more quickly as x decreases or as y decreases? Justify your answer.    The contour graph   and its associated three-dimensional graph are given below. At   will   decrease more quickly as x decreases or as y decreases? Justify your answer.

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Find Find   .  . Find   .

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If If   find   and   . find If   find   and   . and If   find   and   . .

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Consider the point Consider the point   on the contour graph of   given below. When x is decreased by 1, by what amount must y change in order to remain on the same contour curve?  on the contour graph of Consider the point   on the contour graph of   given below. When x is decreased by 1, by what amount must y change in order to remain on the same contour curve?  given below. When x is decreased by 1, by what amount must y change in order to remain on the same contour curve? Consider the point   on the contour graph of   given below. When x is decreased by 1, by what amount must y change in order to remain on the same contour curve?

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The contour graph The contour graph   and its associated three-dimensional graph are given below. At   does   increase when x increases or when x decreases? Justify your answer.    and its associated three-dimensional graph are given below. At The contour graph   and its associated three-dimensional graph are given below. At   does   increase when x increases or when x decreases? Justify your answer.    does The contour graph   and its associated three-dimensional graph are given below. At   does   increase when x increases or when x decreases? Justify your answer.    increase when x increases or when x decreases? Justify your answer. The contour graph   and its associated three-dimensional graph are given below. At   does   increase when x increases or when x decreases? Justify your answer.    The contour graph   and its associated three-dimensional graph are given below. At   does   increase when x increases or when x decreases? Justify your answer.

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