Question

How do you find the average rate of change of y=-2(x^2)+1 over the interval [-1,-0.5] and the instantaneous rate of change at x=-1?

Answer 1

Average rate of change:\[
\frac{y(x_2)-y(x_1)}{x_2-x_1}
\]In this case \(x_2=-0.5\) and \(x_1=-1\).

Answer 2

Instantaneous rate of change:\[
y'(x_0)
\]In this case \(x_0=-1\). Just take the derivative and plug it in.