a)
To find: The possible points at which the tangent to the curve
a)
Answer to Problem 13RE
The point at which the horizontal tangent occurs for the curve
Explanation of Solution
Given information: The equations of the curve are
Formula used: The formulas of differentiation for sine and cosine function are:
The condition for horizontal tangents to the curve occur,
Calculation:
Differentiate the equation
To find if there are any horizontal tangents, substitute
It is evident that at
Substitute
Substitute
Hence, the points at which the horizontal tangent occurs for the curve are
b)
To find: The possible points at which the tangent to the curve
b)
Answer to Problem 13RE
The points at which the vertical tangent occurs for the curve
Explanation of Solution
Given information: The given equations of the curve are
Formula used: The formulas of differentiation for sine and cosine function are:
The condition for vertical tangents to occur,
Calculation:
Divide equation
As the denominator is
Hence, the vertical tangent to the given curves does not exist.
Chapter 10 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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