Find the average rate of change h(x)=2x^2-4 from x=2 to x=6
Simplify your answer as much as possible
average=(finalvalue-initial value)/chngeinX
final value= h'(6)=4*6=24
initial vealue=h'(2)=4*2=8
average h'=16/4=4 units unknown
To find the average rate of change of a function over an interval, you need to calculate the difference in the function values at the endpoints of the interval and divide it by the difference in the input values.
In this case, we are given the function h(x) = 2x^2 - 4 and the interval from x = 2 to x = 6.
Step 1: Calculate the function values at the endpoints.
To find h(2), substitute x = 2 into the function:
h(2) = 2(2)^2 - 4 = 2(4) - 4 = 8 - 4 = 4
To find h(6), substitute x = 6 into the function:
h(6) = 2(6)^2 - 4 = 2(36) - 4 = 72 - 4 = 68
Step 2: Calculate the difference in the function values.
Difference in function values = h(6) - h(2) = 68 - 4 = 64
Step 3: Calculate the difference in the input values.
Difference in input values = 6 - 2 = 4
Step 4: Calculate the average rate of change.
Average Rate of Change = (Difference in function values) / (Difference in input values)
Average Rate of Change = 64 / 4 = 16
Therefore, the average rate of change of h(x) = 2x^2 - 4 from x = 2 to x = 6 is 16.