How do you find the average rate of change of #y = 9x^3  2x^2 + 6# between x = 4 and x = 2?
in order to determine the typical rate of change.
Here, b = 2 and a = 4.
The typical rate of change from (2,70) and (4,550) is
This indicates that between (4,550) and (2,70), the average slope of all the lines tangent to the graph of f(x) is  80.
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To find the average rate of change of ( y = 9x^3  2x^2 + 6 ) between ( x = 4 ) and ( x = 2 ), first calculate the values of the function at ( x = 4 ) and ( x = 2 ), then use the formula for average rate of change:
[ \text{Average rate of change} = \frac{\text{Change in } y}{\text{Change in } x} ]

Substitute ( x = 4 ) into the function: [ y(4) = 9(4)^3  2(4)^2 + 6 ]

Substitute ( x = 2 ) into the function: [ y(2) = 9(2)^3  2(2)^2 + 6 ]

Calculate ( y(4) ) and ( y(2) ).

Calculate the change in ( y ): [ \text{Change in } y = y(2)  y(4) ]

Calculate the change in ( x ): [ \text{Change in } x = 2  (4) ]

Divide the change in ( y ) by the change in ( x ) to find the average rate of change.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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