Plot a Continuous Function Graph: Data Analysis & Solutions

[leprofece]

Plot a continue function graph with the following data o properties f(4)= 0 f of (-2) = 0 f of second derivative in 1 = 0?
f of first derivative in (3) = 0
f de second derivative in 2 =0
2nd derivative (x) > 0 and (1,2)
2nd derivative (x) < 0 in x < 1 and x>2
see my graph is it correct?? where am I wrong??
I got confused because secon and first derivative descipcion in 3 does not match with the data given View attachment 2728m

 

[Evgeny.Makarov]

Plot a continue function graph with the following data o properties f(4)= 0 f of (-2) = 0 f of second derivative in 1 = 0?f de second derivative in 2 =0

What are you trying to achieve using different prepositions and writing conditions on $f$ and its derivatives in four different ways? Please rewrite your conditions as equations of the form
\begin{align*}
f(\dots)=\dots\\
f'(\dots)=\dots\\
f''(\dots)=\dots\\
\end{align*}

 

[soroban]

Hello, leprofece!

Your description is awful!

Sketch a continuous graph with the following properties:

$$\begin{array}{cc}[1] &f(4)\:=\: 0 \\ [2] & f(\text{-}2) \:=\: 0 \\ [3] & f'(3) \:=\: 0 \\ [4] & f''(1) \:=\: 0 \\ [5] & f''(2) \:=\: 0 \\ [6] & f''(x) > 0\,\text{ for }1 < x < 2 \\ [7] &f''(x) < 0\,\text{ for }x < 1\text{ and }x > 2 \end{array}$$

[1] & [2]: $x$-intercepts at $$(4,0),\;(\text{-}2,0)$$

[3]: Max/min when $$x = 3.$$

[4] & [5]: Inflection points when $$x = 1,\;x = 2.$$

[6]: Graph is concave up on $$(1,2)$$

[7]: Graph is concave down elsewhere.The graph looks like this:

                       *
                    *      *
                   *          *
                 *              *
              *
      ----*----------------------*---
        *-2   1    2   3         4 
       *
                                  *
      *