Question

Calculate the instantaneous rate of change at x = -1

Answer 1

The function that describes the graph above looks like this:
$x^2-2x=0$

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:
$f'(x)=(x^2-2x)'=2x-2$

Now, let's replace $x$ variable with given value $(-1)$:
$f'(-1)=2*(-1)-2=-4$

Solution:the instantaneous rate of change at $x = -1$ is -4.