The function that describes the graph above looks like this:
[tex]x^2-2x=0[/tex]
The rate of change at a particular moment is the same as the value of the derivative at a particular point. So, let's find a derivative of your function:
[tex]f'(x)=(x^2-2x)'=2x-2[/tex]
Now, let's replace [tex]x[/tex] variable with given value [tex](-1)[/tex]:
[tex]f'(-1)=2*(-1)-2=-4[/tex]
Solution:the instantaneous rate of change at [tex]x = -1[/tex] is -4.
