Find the points at which the graph of the equation has a vertical or horizontal tangent line.

Question

question on implicit diffrenciation

Answer 1

Whatever the equation is, differentiate.  To find the points on the curve for which there is a horizontal tangent, solve the equation dy/dx = 0. There are vertical tangents at the points on the curve where dy/dx is undefined.

 

Example:  x² + y² = 4

 

Differentiate with respect to x:  2x + 2y(dy/dx) = 0

 

                                                        dy/dx = -x/y

 

Horizontal tangent:  solve dy/dx = 0

 

                                          x = 0 and y = 2 or -2

  

                             Horizontal tangent at (0,2) and (0,-2)

 

Vertical tangent:  dy/dx is undefined when y = 0 (so, x = 2 or x = -2)

 

                             Vertical tangent at (2,0) and (-2,0)

 

 

Answer 2

INADEQUATE INFORMATION...this case is hopeless.