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(a)
To calculate: The derivative of function
(a)
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Answer to Problem 14CT
Solution:
The derivative of the function at
Explanation of Solution
Given information:
The function,
Formula used:
The derivative of the function
Explanation:
As the function is
Therefore,
By using definition of derivative,
Simplifying numerator,
(b)
An equation of tangent line to the graph of
(b)
![Check Mark](/static/check-mark.png)
Answer to Problem 14CT
Solution:
The equation of tangent line to the graph of
Explanation of Solution
Given information:
The function,
Explanation:
To find an equation of tangent line at point
The slope of the tangent line to the graph of
Hence the slope of the tangent line is
The equation of tangent line,
Subtracting
Hence, the equation of tangent line to the graph of
(c)
To graph: The function
(c)
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given Information:
The function,
Graph:
To graph the function
Find
To find
Thus, the
To find
Thus, the
To find vertex of parabola, Compute
Substitute
Thus, the vertex is
Graph of the function using
From part (b),
The equation of tangent line to the graph of
One point on the tangent line is
For other point, substitute
Thus, point is
Plot these two points and draw the tangent line passing through them.
The graph is as below,
Interpretation:
The graph represents the equation of function
Chapter 14 Solutions
Precalculus
Additional Math Textbook Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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Precalculus Enhanced with Graphing Utilities (7th Edition)
Precalculus (10th Edition)
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