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Slopes and Tangentsa. Normal to a curve Find an equation
Chapter 3, Problem 55E(choose chapter or problem)
Problem 55E
Slopes and Tangents
a. Normal to a curve Find an equation for the line perpendicular to the tangent to the curve at the point (2, 1).
b. Smallest slope What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
c. Tangents having specified slope Find equations for the tangents to the curve at the points where the slope of the curve is 8.
Questions & Answers
QUESTION:
Problem 55E
Slopes and Tangents
a. Normal to a curve Find an equation for the line perpendicular to the tangent to the curve at the point (2, 1).
b. Smallest slope What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
c. Tangents having specified slope Find equations for the tangents to the curve at the points where the slope of the curve is 8.
ANSWER:
Solution
Step 1 of 3 Our aim is to find the equation of normal to the given curve at point (2 , 1 )
Given curve is
. . . . . . . . . . (1)
Differentiate with respect to x , we get
. . . . . . . . . . . . . . . . . . (2)
Let be the slope of tangent at point (2,1)
Therefore
As we know that the normal line is perpendicular to the tangent line
Therefore
Slope of tangent slope of normal =
Let be the slope of normal
Hence
So ,
The equation of normal with slope at point (2 ,1 ) is
Solved