# How do you find the average rate of change of #f(x)=2x^2+2# from 4 to 6?

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To find the average rate of change of ( f(x) = 2x^2 + 2 ) from ( x = 4 ) to ( x = 6 ), you use the formula:

[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} ]

where ( a ) and ( b ) are the initial and final values of ( x ), respectively. Substituting the given values:

[ f(4) = 2(4)^2 + 2 = 34 ] [ f(6) = 2(6)^2 + 2 = 74 ]

Then, plug these values into the formula:

[ \text{Average Rate of Change} = \frac{74 - 34}{6 - 4} = \frac{40}{2} = 20 ]

So, the average rate of change of ( f(x) = 2x^2 + 2 ) from ( x = 4 ) to ( x = 6 ) is ( 20 ).

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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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