General statements for the second derivative of a function I am working on a task about second derivative. The task is:
$f(x)$ on $(-1,1)$ has the values $f(-1)=-10$, $f(0)=-10$ and $f(1)=-3$. 
What can you say about the values for first and second derivative?
For the first derivative I use the mean value theorem and find $f'(c)$ for different intervals. 
For the second derivative I have some statements:
1) $|f '' (c)|>\frac{7}{2}$
2) $|f '' (c)|>7$
Are there any theorems or rules I can use in order to check if these statements are true or not? 
Thanks!

Hint
If we consider $x\in(-1,1)$ then 
$$|f'(x)|\le k\implies |f(x)-f(0)|\le k\left|x\right|\le k\implies |f(1)-f(0)|\le k.$$
Since $f(1)-f(0)=7,$ what can we say about $k?$
