11. Communicate Explain how you could
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and
are the <em>farthest</em> from the origin and
is the <em>closest</em> from the origin.
Let be a curve of the form . The distance with respect to origin is found by using the following Pythagorean identity:
(1)
Where is the square distance function.
We can modify (1) as following:
(1b)
Now we apply the First and second derivative tests to determine the minimum and maximum distances from the origin:
First derivative test
Second derivative test
The y-component represents a maximum.
Now we graph the function with the ressource of a graphing tool, we find the following points:
Farthest points: ,
.
Closest points: .
and
are the <em>farthest</em> from the origin and
is the <em>closest</em> from the origin.
To learn more on ellipses, we kindly invite to check this verified question: brainly.com/question/19507943
