Answer
The greatest positive value of the electric potential is $~~40.0~V$
Work Step by Step
We can use Equation (24-21) to find the potential difference between two points:
$\Delta V = -E~\Delta x$
The area under the $E$ versus $x$ graph is the negative of the potential difference.
As we move along the x axis, if the value of $E$ is below the x axis, then the value of the electric potential continues to increase. Thus the value of the electric potential continues to increase until $x = 3.0~m$ which is the point where the electric potential is a maximum.
We can find the area under the graph between $x=0$ and $x = 3.0~m$:
$Area = \frac{1}{2}(-20.0~N/C)(2.0~m)+\frac{1}{2}(-20.0~N/C)(1.0~m)$
$Area = -30.0~V$
The potential difference between $x=0$ and $x = 3.0~m$ is $\Delta V = 30.0~V$
Since the electric potential at the origin is $10~V$, the electric potential at $x = 4.0~m$ is $40.0~V$
The greatest positive value of the electric potential is $~~40.0~V$.
