# What are the points of inflection, if any, of #f(x)= x^4-6x^3 #?

There exists a point of inflection at

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To find the points of inflection of ( f(x) = x^4 - 6x^3 ), we first find the second derivative and then set it equal to zero to solve for the values of ( x ).

First derivative: ( f'(x) = 4x^3 - 18x^2 )

Second derivative: ( f''(x) = 12x^2 - 36x )

Setting the second derivative equal to zero: ( 12x^2 - 36x = 0 )

Factor out 12x: ( 12x(x - 3) = 0 )

Setting each factor equal to zero: ( 12x = 0 ) or ( x - 3 = 0 )

Solving for ( x ): ( x = 0 ) or ( x = 3 )

Therefore, the points of inflection are ( x = 0 ) and ( 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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