Average rate of change of polynomials
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Problem
g(t)= -(t-1)^2 +5g(t)=−(t−1)
2
+5g, left parenthesis, t, right parenthesis, equals, minus, left parenthesis, t, minus, 1, right parenthesis, squared, plus, 5
What is the average rate of change of ggg over the interval -4\leq t\leq 5−4≤t≤5minus, 4, is less than or equal to, t, is less than or equal to, 5?

1

Step-by-step explanation:

g(t)= -(t -1 )² +5

1. Calculate the values of g(-4) and g(5)

g(-4) = -(-4 - 1)² + 5 =  -(-5)² + 5 = -25 + 5 = -20

g(5) = -( 5 - 1)² + 5 =  - (4)² + 5 =  -16 + 5 =  -11

2. Calculate the average rate of change

Rate of change = (y₂ - y₁)/(x₂-x₁) = [-11 -(-20)]/[5 - (-4)] = (-11+ 20)/(5 + 4) = 9/9 = 1

The average rate of change is 1.

In the figure below, the red curve represents the function g(t), while the black dashed line represents the average rate of change over the interval [-4,5].