Horizontal Tangent Line

Proposition (Horizontal Tangent Line) If then the equation of the tangent line to the curve at the point is and is said to have a horizontal tangent line at

Example (Horizontal Tangent Line) For what values of does the graph of have a horizontal tangent?

    Solution. To find the horizontal tangent lines we find where the derivative is 0. We compute, So we need to solve We find,  





And using the quadratic formula we have Thus, the values of 9x0 where the tangents lines are horizontal are
    
Example (Horizontal Tangent Line)  Find the points on the curve where the tangent line is horizontal.

    Solution. To find the horizontal tangent lines we find where the derivative is 0. We compute, So we need to solve Using the quadratic formula we have and Thus, the values of where the tangents lines are horizontal are and   

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Horizontal Tangent Lines
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/horizontal-tangent-lines.html