Question
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.
rate of -6 units per minute. How fast is the
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
Upstudy AI Solution
Tutor-Verified Answer
Answer
The
-coordinate is changing at a rate of
units per minute.
Solution

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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.