Question
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A point is moving along the graph of . When the point is at , its -coordinate is changing at the
rate of -6 units per minute. How fast is the -coordinate changing at that moment?
The y-coordinate is changing by
(Type an integer or a fraction. Simplif
units.
units per minute.

Ask by Griffiths Pierce. in the United States
Nov 09,2024

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Answer

The -coordinate is changing at a rate of units per minute.

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Beyond the Answer

To find the rate of change of the -coordinate at the point , we can use implicit differentiation on the equation .
Differentiating both sides with respect to time :
Using the product rule, we have:
Now, substituting , , and :
Calculating , , and :
Thus, the -coordinate is changing at a rate of units per minute.

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