Concept explainers
(a)
To find: The slope of the curve
(a)
Answer to Problem 11E
The slope of the curve
Explanation of Solution
Given information:
The curve is
Calculation:
The formula for the slope of the curve
The slope of the curve
Substitute
Substitute
Substitute
Further simplify,
Therefore, the slope of the curve
(b)
To find: The equation of the tangent line to the curve
(b)
Answer to Problem 11E
The equation of the tangent line to the curve
Explanation of Solution
Given information:
The curve is
Calculation:
The equation of the tangent line to
The function is
Substitute
Therefore, the equation of the tangent line to the curve
(c)
To find: The equation to the normal line of the curve
(c)
Answer to Problem 11E
The equation of the normal line to the curve
Explanation of Solution
Given information:
The curve is
Calculation:
The equation of the normal line of
The function is
So, the slope of the normal to the curve
Substitute
Therefore, the equation of the normal line to the curve
(d)
To graph: The curve
(d)
Explanation of Solution
Given information:
The curve is
Graph:
As calculated in part (b), the equation of the tangent line to the curve
As calculated in part (c), the equation of normal line to the curve
To graph the curve, tangent and normal to the curve, follow the steps using graphing calculator.
First press “ON” button on graphical calculator, press
The display will show the equations,
Now, press the
Figure (1)
Interpretation: From the graph it can be seen that the curve, the tangent and the normal line intersect the upper half of the curve at the point
Chapter 2 Solutions
Calculus: Graphical, Numerical, Algebraic
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (3rd Edition)
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Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Calculus and Its Applications (11th Edition)
University Calculus: Early Transcendentals (4th Edition)
Calculus & Its Applications (14th Edition)
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