# Is #f(x)=(x-2)(x+5)(x+2)# increasing or decreasing at #x=-3#?

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To determine if the function ( f(x) = (x - 2)(x + 5)(x + 2) ) is increasing or decreasing at ( x = -3 ), we need to analyze the sign of the derivative at that point.

- Compute the derivative of ( f(x) ) using the product rule.
- Evaluate the derivative at ( x = -3 ).
- If the derivative is positive at ( x = -3 ), the function is increasing at that point. If it's negative, the function is decreasing.

Let's perform these steps:

- ( f'(x) = (x + 5)(x + 2) + (x - 2)(x + 2) + (x - 2)(x + 5) ).
- ( f'(-3) = (2)(-1) + (-5)(-1) + (-5)(2) = -2 + 5 - 10 = -7 ).
- Since ( f'(-3) = -7 ) (negative), the function is decreasing at ( x = -3 ).

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