# Is #f(x)=(-x-4)^2+3x^2-3x # increasing or decreasing at #x=-1 #?

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To determine if the function ( f(x) = (-x - 4)^2 + 3x^2 - 3x ) is increasing or decreasing at ( x = -1 ), we need to evaluate the sign of the derivative of the function at that point.

First, find the derivative of ( f(x) ) with respect to ( x ):

( f'(x) = 2(-x - 4)(-1) + 6x - 3 )

Now, evaluate ( f'(-1) ):

( f'(-1) = 2(-(-1) - 4)(-1) + 6(-1) - 3 )

( f'(-1) = 2(-(-1) - 4)(-1) - 6 - 3 )

( f'(-1) = 2(-1 + 4)(-1) - 6 - 3 )

( f'(-1) = 2(3)(-1) - 6 - 3 )

( f'(-1) = -6 - 6 - 3 )

( f'(-1) = -15 )

Since the derivative ( f'(-1) = -15 ) is negative, the function ( f(x) ) is decreasing at ( x = -1 ).

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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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