Thread: draw curve

Sketch the grah of a continuous function f that satisfies all of the stated conditions.

f(0) =2;f(-2) = f(2)=0; f^1(-2) = f^1(0)=f^l(2)=0;
f^l(x)> 0 if -2 <x<0;f^1(x)<0 if x<-2 or x>0;
f^ll(x) > 0if x<-1 or 1 <x<2;
f^ll(x) < 0 if -1<x<1 or x>2

Okay this problem has got me in a wirl wind of fire. Step-by-step help please.

i don't understand how to start the problem but do you start with derivatives

Hello, uniquereason81!

Sketch the grah of a continuous function
that satisfies all of the stated conditions.

[1] gives us three points: . 0,2),\2,0)" alt="(-2,0),\0,2),\2,0)" />

[2] tells that the tangents are horizontal at those three points

Code:

                 2|
                 =o=
                  |
                  |
                  |
      - =o= - - - + - - - =o= - -
         2        |        2
                  |

[3] tells us that the curve is uphill on [-2.0]
[4] says it is downhill everywhere else.

Code:

 
                  |
                  *
                / | \
     \        /   |   \
       \    /     |     \
      - -*- - - - + - - - -*- -
        -2        |        2 \
                  |           \ 
                  |

[5] tells us the curve is concave up to the left of -1, and on [1,2]

Code:

                  |
    *             *
                / |  \
     *        /   |    *
      *     *     |     *
    - - -*- -+- - + - -+- -*- -
        -2  -1    |    1   2\
                  |          \ 
                  ||

[6] says the curve is concave down everywhere else.

Code:

                  |
    *             *
               *  |  *
     *       *    |    *
      *     *     |     *
    - - -*- -+- - + - -+- -*- - - -
         2  -1    |    1   2   *
                  |              * 
                  |               *
                  |

There!

wow thanks alot