# How do you find the average rate of change for the function #f(x) = x^2 - 2x # on the indicated intervals [1,3]?

The average rate of change of function

In light of this, we have

Moreover, the typical rate of change is

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To find the average rate of change of the function ( f(x) = x^2 - 2x ) on the interval ([1,3]), you need to calculate the difference in the function values at the endpoints of the interval and then divide by the difference in the input values.

( f(1) = (1)^2 - 2(1) = 1 - 2 = -1 )

( f(3) = (3)^2 - 2(3) = 9 - 6 = 3 )

The average rate of change is:

[ \frac{{f(3) - f(1)}}{{3 - 1}} = \frac{{3 - (-1)}}{{3 - 1}} = \frac{4}{2} = 2 ]

So, the average rate of change of ( f(x) = x^2 - 2x ) on the interval ([1,3]) is ( 2 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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