# What are the points of inflection, if any, of #f(x) =x^3 - 12x^2 #?

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To find the points of inflection, we need to determine where the concavity changes. We find the second derivative of ( f(x) = x^3 - 12x^2 ) and solve for where it equals zero.

First derivative: ( f'(x) = 3x^2 - 24x ) Second derivative: ( f''(x) = 6x - 24 )

Setting ( f''(x) ) equal to zero and solving for ( x ): ( 6x - 24 = 0 ) ( 6x = 24 ) ( x = 4 )

So, the point of inflection is at ( x = 4 ).

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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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