What is the instantaneous rate of change of #f(x)=(x-1)^2-4x# at #x=0#?
Instantaneous rate of change at x=0 of f(x) is -6.
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To find the instantaneous rate of change of ( f(x) = (x - 1)^2 - 4x ) at ( x = 0 ), we need to compute the derivative of the function and then evaluate it at ( x = 0 ). The derivative of ( f(x) ) is found using the power rule and the chain rule:
[ f'(x) = 2(x - 1)(1) - 4 = 2x - 2 - 4 = 2x - 6 ]
Now, to find the instantaneous rate of change at ( x = 0 ), substitute ( x = 0 ) into ( f'(x) ):
[ f'(0) = 2(0) - 6 = -6 ]
Therefore, the instantaneous rate of change of ( f(x) ) at ( x = 0 ) is ( -6 ).
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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.
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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