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

Increasing.

We compute the slope of the function by finding the first derivative. To do this we shall use the quotient rule:

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To determine if ( f(x) = \frac{-2x^2 - 4x - 2}{2x^2 + 1} ) is increasing or decreasing at ( x = -3 ), we evaluate the derivative of the function at that point. If the derivative is positive, the function is increasing at that point. If the derivative is negative, the function is decreasing at that point.

The derivative of ( f(x) ) can be found using the quotient rule:

[ f'(x) = \frac{(2x^2 + 1)(-4x - 4) - (-2x^2 - 4x - 2)(4x)}{(2x^2 + 1)^2} ]

Evaluating ( f'(-3) ) will determine if the function is increasing or decreasing at ( x = -3 ).

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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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