How to find instantaneous rate of change for #f(x)=x^3x^22x 4# at x=2?
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To find the instantaneous rate of change for the function ( f(x) = x^3  x^2  2x ) at ( x = 2 ), we need to find the derivative of the function and then evaluate it at ( x = 2 ).

Find the derivative of the function ( f(x) ): [ f'(x) = \frac{d}{dx}(x^3  x^2  2x) ] [ = 3x^2  2x  2 ]

Evaluate the derivative at ( x = 2 ): [ f'(2) = 3(2)^2  2(2)  2 ] [ = 3(4)  4  2 ] [ = 12  4  2 ] [ = 6 ]
Therefore, the instantaneous rate of change of the function ( f(x) ) at ( x = 2 ) is ( 6 ).
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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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