# Is #f(x)=(x-3)^3+3x^2-2x # increasing or decreasing at #x=0 #?

Hence,

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To determine whether ( f(x) = (x - 3)^3 + 3x^2 - 2x ) is increasing or decreasing at ( x = 0 ), we need to analyze the sign of the first derivative ( f'(x) ) at that point.

( f'(x) ) is the derivative of ( f(x) ) with respect to ( x ).

( f'(x) = 3(x - 3)^2 + 6x - 2 ).

Evaluate ( f'(0) ).

( f'(0) = 3(0 - 3)^2 + 6(0) - 2 ).

( f'(0) = 3(9) - 2 ).

( f'(0) = 27 - 2 = 25 ).

Since ( f'(0) = 25 > 0 ), the function is increasing at ( x = 0 ).

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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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