Answer
See the detailed answer below.
Work Step by Step
We also know that
$$E_x=-\dfrac{dV}{dx}\tag 1$$
which is negative the slope of the $V-x$ graph.
We have 3 stages of the given graph.
$$\color{blue}{\bf [a]}$$
At $x=-2$ cm, which is in the first stage,
From (1),
$$E_x=-\dfrac{-10-0}{-1-(-3)} =\color{red}{\bf 5}\;\rm V/m$$
$$\color{blue}{\bf [b]}$$
At $x=0$ cm, which is in the second stage,
From (1),
$$E_x=-\dfrac{10-(-10)}{ 1-(-1)} =\color{red}{\bf -10}\;\rm V/m$$
$$\color{blue}{\bf [c]}$$
At $x=2$ cm, which is in the third stage,
From (1),
$$E_x=-\dfrac{0-10}{ 3-1} =\color{red}{\bf 5}\;\rm V/m$$
