Could you help me with the following please:

Give an example of a differentiable function $f:\mathbb{R} \rightarrow \mathbb{R}$ that has a point $c$ such that $f'(c)$ is not equal to the difference quotient $\dfrac{f(b)-f(a)}{b-a}$ for any $a<b$. Why does this not contradict the mean value theorem?

In a graphical way what can be seen is that this occurs when the second derivative of $ f $ is 0, but trying to find this function, I have considered a polynomial with this property, but I cannot see that it fulfills this characteristic. One attempt has been to consider the $ f(x)=x^3+3x+2 $, but it failed to conclude that this is an example of what the exercise asks of us.

And well, I think this does not contradict the MVT for the domain of said function.