Slopes and Tangents1. Horizontal Tangents Find equations

Chapter 3, Problem 56E

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QUESTION:

Problem 56E

Slopes and Tangents

Horizontal Tangents    Find equations for the horizontal tangents to the curve Also find equations for the line that are perpendicular to these tangents at the points of tangency.Smallest Slope    What is the smallest slope on the curve? At what point on the curve does the curve have this slope? Find an equation for the line that is perpendicular to the curve’s tangent at this point.

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QUESTION:

Problem 56E

Slopes and Tangents

Horizontal Tangents    Find equations for the horizontal tangents to the curve Also find equations for the line that are perpendicular to these tangents at the points of tangency.Smallest Slope    What is the smallest slope on the curve? At what point on the curve does the curve have this slope? Find an equation for the line that is perpendicular to the curve’s tangent at this point.

ANSWER:

Solution Our aim is to find the horizontal tangent and the smallest slope on the given curve

Step 1 of 3 Given curve is

 . . . . . . . . . . . . (1)

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