Determine the average rate of change of f(x)=1/(x^2 -x) over the
interval 2 is less then or equal to x and 3 is greater or equal to x.
average rate of change= f(3)-f(2) / (3-2)= 1/6-1/2=-1/3
all those words!! Why not just
2 <= x <= 3
or even better,
[2,3]
thanks that's a better way to write it
To determine the average rate of change of a function over a given interval, we use the formula:
Average Rate of Change = (f(b) - f(a)) / (b - a)
Where 'f(b)' represents the value of the function at the upper limit of the interval, 'f(a)' represents the value of the function at the lower limit of the interval, 'b' is the upper limit, and 'a' is the lower limit.
In this case, the lower limit is 2 (a = 2) and the upper limit is 3 (b = 3). We need to calculate f(3) and f(2) to find the average rate of change.
Let's calculate:
f(3) = 1 / (3^2 - 3) = 1 / (9 - 3) = 1 / 6
f(2) = 1 / (2^2 - 2) = 1 / (4 - 2) = 1 / 2
Now, we can substitute these values into the average rate of change formula:
Average Rate of Change = (f(3) - f(2)) / (3 - 2)
Substituting the calculated values:
Average Rate of Change = (1/6 - 1/2) / (3 - 2)
To simplify further, we need to find a common denominator:
Average Rate of Change = [(1 - 3)/6] / 1
Now, subtract the numerator of the fraction:
Average Rate of Change = (-2/6) / 1
Finally, simplify the expression:
Average Rate of Change = -2/6 = -1/3
Therefore, the average rate of change of f(x) = 1/(x^2 - x) over the interval where 2 ≤ x ≤ 3 is -1/3.