Calculate the average rate of change of the given function over the given interval. Where appropriate, specify the units of measurement.
f(x) = 1/x;[2, 7]
I used the f(b)-f(a)/b-a and I got -.071 and it said I was wrong could you please help me find my error?
WROK:
y1= 1/x (put this for my y-value in my calculator
then (y1(7)-y1(2))/(7-2) which equals -.071
thank you apparently that is all I had to do=)
To calculate the average rate of change of a function over a given interval, you need to find the change in the function values divided by the change in the input values.
Let's use the formula you mentioned: average rate of change = (f(b) - f(a)) / (b - a)
For the given function f(x) = 1/x over the interval [2, 7], we can substitute the values:
f(a) = f(2) = 1/2
f(b) = f(7) = 1/7
a = 2
b = 7
Now let's substitute these values into the formula:
Average rate of change = (1/7 - 1/2) / (7 - 2)
To simplify, we need to find a common denominator for the fractions:
Average rate of change = ((1*2 - 1*7) / (7*2)) / (7 - 2)
= (-5/14) / 5
= -5/14 * 1/5
= -1/14
Therefore, the average rate of change of the function f(x) = 1/x over the interval [2, 7] is -1/14. The units of measurement depend on the context of the function, so in this case, they would be the reciprocal of the units of x.
It seems that your calculation error could be due to either incorrect arithmetic or not simplifying the fraction. Double-check your calculations to find the error.
f(2) = 1/2
f(7) = 1/7
avg rate of change = (1/7 - 1/2)/(7-2)
= (-5/14)/5)
= -1/14
don't go with decimals, they are not accurate,
stay with fractions for exact answers.