(a)
To determine: The points at which the tangent to the curve is horizontal.
(a)
Answer to Problem 11RE
The required points are
Explanation of Solution
Given information:
The equations:
Formula used:
Formulas of derivatives:
Calculation:
The given equations are
And,
Write the point at which the tangent to the curve is horizontal as:
Find derivative of equation (1) and equation (2) with respect to t .
And,
Now,
It is known that a tangent to the curve is horizontal if
Substitute 0 for
Simplify the above expression for t .
Substitute 0 for t in the point
Also, substitute
Hence, the required points are
(b)
To determine: The points at which the tangent to the curve is vertical.
(b)
Answer to Problem 11RE
The tangent to the curve is not vertical at any point.
Explanation of Solution
Given information:
The equations:
Formula used:
Formulas of derivatives:
Calculation:
The given equations are
And,
Write the point at which the tangent to the curve is horizontal as:
Find derivative of equation (1) and equation (2) with respect to t .
And,
Now,
It is known that a tangent to the curve is vertical if
Substitute 0 for
Since, t has no value for which
Hence, the tangent to the curve is not vertical at any point.
Chapter 11 Solutions
Calculus: Graphical, Numerical, Algebraic
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