Suppose we have function $f(x)$ that is continious and it has first and second order derivatives and its table likes the following. $\ \begin{array}{ c|c|c|} & x< 0 & x >0\\ \hline f' & - & +\\ f'' & - & - \end{array}$
Question is " Why it is not possible to have such a graph of a function? "
- My attempts: I thought that if I have the following table $\ \begin{array}{ c|c|c|} & x< 0 & x >0\\ \hline f' & - & +\\ f'' & + & + \end{array}$ then I can say that function can be $f(x)=x^2$. But for above, again I thought that maybe function can be $-x^2$ which satisfies the conditions of table which is totally wrong. So, can you help me to figure out the question? Gracias