Find the average rate of change of g(x)=−5x2−1𝑔(𝑥)=-5𝑥2-1 on the interval [−1,3][-1,3] .

The average rate of change of a function on the interval [a, b] is given by the formula:

(f(b) - f(a)) / (b - a)

Here, our function is g(x) = -5x^2 - 1 and our interval is [-1, 3]. So, we need to find g(-1) and g(3).

First, let's find g(-1): g(-1) = -5(-1)^2 - 1 = -5 - 1 = -6

Next, let's find g(3): g(3) = -5(3)^2 - 1 = -5*9 - 1 = -45 - 1 = -46

Now, we can find the average rate of change: (f(b) - f(a)) / (b - a) = (g(3) - g(-1)) / (3 - (-1)) = (-46 - (-6)) / (3 - (-1)) = (-46 + 6) / 4 = -40 / 4 = -10

So, the average rate of change of the function g(x) = -5x^2 - 1 on the interval [-1, 3] is -10.