To determine: The correct option for the parametric curve to be,
(A) increasing and concave up.
(B) increasing and concave down.
(C) decreasing and concave up.
(D) decreasing and concave down.
(E) decreasing with a point of inflection.
Answer to Problem 48E
The correct option is (C).
Explanation of Solution
Given information:
The parametric equations:
Calculation:
The parametric equations are
It is known that
So,
Substitute
This means the curve is decreasing.
Now, differentiate the expression
Again, differentiate the above derivative.
It is seen that the second derivative is positive. This means that the curve is concave up.
Thus, the curve is decreasing and concave up.
Hence, the correct option is (C).
Chapter 11 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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