To determine: The equations for the horizontal and vertical tangent lines to the curves.
Answer to Problem 23RE
The required tangents are
Explanation of Solution
Given information:
The equation:
Formula used:
Product rule of differentiation:
Calculation:
The given equation is
It is seen that in polar
Rewrite the coordinates as:
Here, the slope of the tangent is,
It is known that for a tangent line to be horizontal, the slope of the line is 0.
Simplify the above expression further.
From the above equation we get the tangents as:
Now, it is known that for a tangent line to be vertical, the slope of the line is undefined.
Simplify the above expression further.
From the above equation we get the tangents as:
Hence, the required tangents are
Chapter 11 Solutions
Calculus: Graphical, Numerical, Algebraic
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