How can I plot the vector field of a differential equation on the real line?

Question

I´m trying to plot:

for the differential equation $x'=4x^2-16$ in matlab. I have tried so many things but I can´t come to a solution. I appreciate the help!

Answer 1

I don't know how to do it in matlab, but I drew the graph of the function in geogebra and it looks like this:

For $x<-2$ you have $x'>0$, so the arrow goes to the left.

For $-2<x<2$ you have $x'>0$, so the arrow goes to the right.

For $x>2$ you have $x'>0$, so the arrow goes to the left.