# How do you find the average rate of change for the function #s(t)=4.5t^2# on the indicated intervals [6,12]?

Average Rate of Change = 81

Therefore, this function's average rate of change is

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To find the average rate of change of the function ( s(t) = 4.5t^2 ) on the interval ([6, 12]), you calculate the difference in the function values at the endpoints of the interval and divide by the difference in the input values.

First, find the function values at the endpoints: ( s(6) = 4.5(6)^2 = 162 ) ( s(12) = 4.5(12)^2 = 648 )

Next, calculate the difference in function values: ( 648 - 162 = 486 )

Then, calculate the difference in input values: ( 12 - 6 = 6 )

Finally, divide the difference in function values by the difference in input values to find the average rate of change: ( \frac{486}{6} = 81 )

So, the average rate of change of the function ( s(t) = 4.5t^2 ) on the interval ([6, 12]) is ( 81 ).

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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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