(a)
To find: The slope of the curve
(a)
Answer to Problem 47RE
The slope of the curve of the function
Explanation of Solution
Given information: The given curve is
Calculation:
Substitute 1 for
So, the given point is
Therefore, the slope of the curve of the function
(b)
To find: The equation of the tangent at
(b)
Answer to Problem 47RE
The equation of the tangent is
Explanation of Solution
Given information: The given curve is
Formula used: The equation of a tangent that passes through the point
Calculation:
From part (a), the point is
The equation of the tangent at
Therefore, the equation of the tangent is
(c)
To find: The equation of the normal at
(c)
Answer to Problem 47RE
The equation of the normal is
Explanation of Solution
Given information: The given curve is
Formula used: The equation of a normal that passes through the point
Calculation:
From part (a), the slope of the tangent is
It is known that tangent and normal are perpendicular to each other.
The equation of normal that passes through the point
Therefore, the equation of the normal is
Chapter 2 Solutions
Calculus: Graphical, Numerical, Algebraic
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