(a)
The equation of the tangent line to the graph of
(a)
Answer to Problem 17E
The required equation of the tangent line is
Explanation of Solution
Given information:
The functions:
Formula used:
It is given that
Also at
This means the slope of the tangent line is 5 and the line passes through the point
To find the equation of the tangent, use point-slope formula of an equation of a line
Substitute 5 for m , 3 for
Hence, the required equation of the tangent line is
(b)
The equation of the normal line to the graph of
(b)
Answer to Problem 17E
The required equation of the normal line is
Explanation of Solution
Given information:
The functions:
Formula used:
Point-slope form of the equation of a line:
It is given that
Also at
This means the slope of the tangent line is 5 and a point on the normal line is
It is known that the normal line is perpendicular to the tangent line at the point of tangency.
So, the slope of the normal line is the negative reciprocal of the slope of the tangent line.
This means slope of the normal line is
To find the equation of the normal line, use the point-slope form of the equation of a line
Substitute
Hence, the required equation of the normal line is
Chapter 3 Solutions
Calculus: Graphical, Numerical, Algebraic
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