Find the average rate of change of h (x)=2x squared-7x from x=1 to x=5. Simpifily your answer as much as possible.
h(x) = 2x^2-7x
the average rate of change is just the slope of the line from (1,h(1)) to (5,h(5)). That is,
(h(5)-h(1))/(5-1)
The answer has to be a simplified whole number
So go ahead and simplify the expression that Steve gave you.
To find the average rate of change of a function, you need to calculate the difference in the function's values between two specific input values and then divide that by the difference in the input values.
In this case, the function is h(x) = 2x^2 - 7x, and we want to find the average rate of change from x = 1 to x = 5.
Step 1: Calculate h(1):
Replace x with 1 in the function:
h(1) = 2(1)^2 - 7(1) = 2 - 7 = -5
Step 2: Calculate h(5):
Replace x with 5 in the function:
h(5) = 2(5)^2 - 7(5) = 2(25) - 35 = 50 - 35 = 15
Step 3: Find the difference in function values:
Difference = h(5) - h(1) = 15 - (-5) = 15 + 5 = 20
Step 4: Find the difference in input values:
Difference in input values = 5 - 1 = 4
Step 5: Calculate the average rate of change:
Average rate of change = Difference in function values / Difference in input values = 20 / 4 = 5
Therefore, the average rate of change of h(x) from x = 1 to x = 5 is 5.