Final answer:
To find the average rate of change of the function g(x)=-x²+4x+9 over the interval -2<=x<=4, plug in the given x-values into the function, calculate the differences in the function values and x-values, and divide them to find the average rate of change.
Step-by-step explanation:
To find the average rate of change of the function g(x)=-x²+4x+9 over the interval -2<=x<=4, we need to calculate the difference in the function values divided by the difference in the x-values.
Step 1: Plug in -2 and 4 into the function to find the corresponding function values:
g(-2) = -(-2)² + 4(-2) + 9 = -4 + (-8) + 9 = -3
g(4) = -(4)² + 4(4) + 9 = -16 + 16 + 9 = 9
Step 2: Calculate the difference in the function values:
Δy = 9 - (-3) = 12
Step 3: Calculate the difference in the x-values:
Δx = 4 - (-2) = 6
Step 4: Calculate the average rate of change:
Average Rate of Change = Δy / Δx = 12 / 6 = 2
Therefore, the average rate of change of the function g(x)=-x²+4x+9 over the interval -2<=x<=4 is 2.