Does a hyperbola y = 1/x have stationary points?

[Guest]

In calculus this only occurs when the first derivative = 0

-1/x^2 = 0 gives no solution. Does this mean that the hyperbola function has
no stationary points?

 

[soroban]

Hello, americo74!

Yes, you are correct.

If you graph or sketch the curve, you'll see it clearly.

                      |
                      |*
                      |
                      | *
                      |  *
                      |    *
                      |        *
                      |              *
      - - - - - - - - + - - - - - - - - - - 
        *             |
             *        |
                 *    |
                   *  |
                    * |
                      |
                     *|
                      |

Both the x-axis and the y-axis are asymptotes.
\(\displaystyle \;\;\)There are no maximum or minimum points.

 

[Guest]

thank you Soroban

you are a star