To find: The equation of the tangent line to the given equation at the point.
Answer to Problem 26E
The equation of the tangent line to the equation
Explanation of Solution
Given:
The curve is
The point is
Derivative rules: Chain rule
If
Formula used:
The equation of the tangent line at
Where, m is the slope of the tangent line at
Calculation:
Consider the equation
Differentiate the given equation implicitly with respect to x,
Apply the chain rule and simplify the terms,
Separate
Therefore, the derivative of the equation is
The slope of the tangent line at the point
Thus, the slope of the tangent line at
Substitute
Therefore, the equation of the tangent line to the equation
Graph:
The graph of the curve and the tangent line is shown below in Figure 1.
From Figure 1, it is observed that the line
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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