How do you find the average rate of change of #f(x)=2x^2+2# from 1 to 1?
Average Rate of Change:
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To find the average rate of change of ( f(x) = 2x^2 + 2 ) from ( x = 1 ) to ( x = 1 ), you first need to calculate the values of ( f(x) ) at the endpoints of the interval. Then, you find the difference in the function values and divide it by the difference in the input values.

Calculate ( f(1) ):
( f(1) = 2(1)^2 + 2 = 2(1) + 2 = 2 + 2 = 4 ) 
Calculate ( f(1) ):
( f(1) = 2(1)^2 + 2 = 2(1) + 2 = 2 + 2 = 4 ) 
Find the difference in function values:
( f(1)  f(1) = 4  4 = 0 ) 
Find the difference in input values:
( 1  (1) = 1 + 1 = 2 ) 
Calculate the average rate of change:
( \text{Average Rate of Change} = \frac{f(1)  f(1)}{1  (1)} = \frac{0}{2} = 0 )
Therefore, the average rate of change of ( f(x) = 2x^2 + 2 ) from ( x = 1 ) to ( x = 1 ) is 0.
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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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