What will be the average rate of change of the function [y = 16 – x2] at x = 4?

The correct option is -8.

To find the rate of change of the function at a single specific point $x=4$, we calculate the instantaneous rate of change, which is given by the derivative of the function with respect to $x$.

The given function is:

$$y=16-x^2$$

Differentiating $y$ with respect to $x$ gives us the rate of change function:

$$\frac{dy}{dx}=\frac{d}{dx}(16-x^2)$$

Using the basic rules of differentiation (where the derivative of a constant is 0, and the power rule is applied to the second term):

$$\frac{dy}{dx}=0-2x=-2x$$

To find the rate of change at $x=4$, we substitute this value into the derivative:

$${\left(\frac{dy}{dx}\right)}_{x=4}=-2\left(4\right)=-8$$

Therefore, the rate of change of the function at $x=4$ is $-8$.