# Is #f(x)=(-x^3-7x^2-x+2)/(x-2)# increasing or decreasing at #x=3#?

Determine whether the function's derivative is positive or negative at that point to ascertain whether a function is increasing or decreasing at that point.

To put it simply,

graph{(x-2))=0 [1.423, 4.492, -91.816, -90.28]}

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To determine if (f(x) = \frac{-x^3 - 7x^2 - x + 2}{x - 2}) is increasing or decreasing at (x = 3), we can use the first derivative test. Calculate (f'(x)) and evaluate it at (x = 3). If (f'(3) > 0), then (f(x)) is increasing at (x = 3). If (f'(3) < 0), then (f(x)) is 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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