We have #f:RR>RR;f(x)=x(x2)#.Is #f# differentiable on #x=2#?
Yes.
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To determine if the function ( f(x) = x(x  2) ) is differentiable at ( x = 2 ), we need to check if the derivative exists at that point.

Calculate the derivative of ( f(x) ): [ f'(x) = \frac{d}{dx}(x(x  2)) = \frac{d}{dx}(x^2  2x) = 2x  2 ]

Evaluate the derivative at ( x = 2 ): [ f'(2) = 2(2)  2 = 4  2 = 2 ]
Since the derivative ( f'(2) ) exists and is finite, the function ( f(x) = x(x  2) ) is differentiable at ( x = 2 ).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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