Question

Question 10
What is the average rate of change of



f(x)=x2−x+4



from x=2 to x=4 ?

Answer 1

To find the average rate of change of a function, we need to calculate the difference in the function values divided by the difference in the input values.

First, let's find the function values at x=2 and x=4:

f(2) = (2)^2 - 2 + 4 = 4 - 2 + 4 = 6
f(4) = (4)^2 - 4 + 4 = 16 - 4 + 4 = 16

Next, let's calculate the difference in the function values:

f(4) - f(2) = 16 - 6 = 10

Finally, let's calculate the difference in the input values:

4 - 2 = 2

Now, we can determine the average rate of change:

Average rate of change = difference in function values / difference in input values
Average rate of change = 10 / 2
Average rate of change = 5

Therefore, the average rate of change of f(x)=x^2-x+4 from x=2 to x=4 is 5.