what is the average rate of change of the following function on the interval -4,9? f(x)={x + 1 -∞ < x ≤ 0…

what is the average rate of change of the following function on the interval -4,9? f(x)={x + 1 -∞ < x ≤ 0 -x² 5 ≤ x < ∞ -6 -1/6 6 1/6

what is the average rate of change of the following function on the interval -4,9? f(x)={x + 1 -∞ < x ≤ 0 -x² 5 ≤ x < ∞ -6 -1/6 6 1/6

Answer

Explanation:

Step1: Find (f(-4))

Since (-4<0), use (f(x)=x + 1). So (f(-4)=-4 + 1=-3).

Step2: Find (f(9))

Since (9\geq5), use (f(x)=-x^{2}). So (f(9)=-9^{2}=-81).

Step3: Calculate average rate of change

The formula for average rate of change of a function (y = f(x)) on ([a,b]) is (\frac{f(b)-f(a)}{b - a}). Here (a=-4), (b = 9), (f(-4)=-3) and (f(9)=-81). Then (\frac{f(9)-f(-4)}{9-(-4)}=\frac{-81-(-3)}{9 + 4}=\frac{-81 + 3}{13}=\frac{-78}{13}=-6).

Answer:

-6