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How to find instantaneous rate of change for #f(x)=x^3-x^2-2x 4# at x=2?

Answer 1

Scarlett Allison

#f'(2)=6#

#f(x) =x^3 -x^2-2x+or-4#

#f'(x) =3x^2-2x-2#

#f'(2)=12-4-2=6#

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Answer 2

William Abdalla

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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Answer from HIX Tutor

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.