To find: The equation of the tangent line to the given equation at the point.
Answer to Problem 28E
The equation of the tangent line to the equation
Explanation of Solution
Given:
The curve is
The point is
Derivative rules:
(1) Chain rule: If
(2) Product rule:
Formula used:
The equation of the tangent line at
Where, m is the slope of the tangent line at
Calculation:
Obtain the equation of the tangent line to the equation at the point.
Rewrite the given equation as follows,
Differentiate the equation implicitly with respect to x,
Apply the chain rule (1) and simplify the terms,
Substitute
Thus, the slope of the tangent at
Substitute
Therefore, the equation of the tangent line to the equation
Graph:
The graph of the given curve and tangent line is shown below Figure 1.
From Figure 1, it is observed that the line
Chapter 3 Solutions
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