To calculate: The equation of tangent line to the curve
Answer to Problem 28E
The equation of tangent line to the curve
Explanation of Solution
Given information:
The equation of curve
Formula used:
Power rule for differentiation is
The point slope form of an equation is
Calculation:
Consider the equation of curve
Differentiate both sides with respect to x ,
Recall that quotient rule for differentiation is
Apply it.
Recall that the point slope form of an equation is
It is provided that the curve passes through the point
Substitute x as 1, in the derivative found above,
Therefore, slope is
Now, the equation of tangent line to the curve
Thus, the equation of tangent line to the curve
It is provided that the curve passes through the point
Substitute xas
Therefore, slope is
Now, the equation of tangent line to the curve
Thus, the equation of tangent line to the curve
Now, use a graphing window to plot the function and its tangent lines. Sketch the graph of
The blue curve depicts the graph of
Observe that the both the lines
The line
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning