(a)
To determine: The points at which the tangent to the curve is horizontal.
(a)
Answer to Problem 13RE
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
Here, at the points
So, the value of t are
Substitute
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 13RE
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
But, at the points
Hence, the tangent to the curve is not vertical at any point.
Chapter 11 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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