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

Decreasing.

Following simplification,

The gradient is downward.

lowering.

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

First, find the derivative of ( f(x) ) with respect to ( x ), which is ( f'(x) ).

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

Now, substitute ( x = -2 ) into the derivative to find the slope at ( x = -2 ).

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

Since the derivative ( f'(-2) ) is negative, this indicates that ( f(x) ) is decreasing at ( x = -2 ).

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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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