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

Decreasing.

A function's first derivative's sign (positive or negative) indicates whether the function is increasing or decreasing at a given point.

Apply the power rule to determine the function's derivative.

We can examine a graph to confirm:

graph{x^2–3x [-7, -4.02, 21.65]}

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

The derivative of the function ( f(x) = x^2 - 3x ) is ( f'(x) = 2x - 3 ).

Evaluate ( f'(-2) ):

[ f'(-2) = 2(-2) - 3 = -4 - 3 = -7 ]

Since the derivative ( f'(-2) ) is negative, the function 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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