# How do you find the inflection points for #f(x)=x^4# ?

The following is the definition of inflection points by James Stewart.

By taking derivatives,

Since

Hence,

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To find the inflection points for ( f(x) = x^4 ), you need to find the second derivative of the function and then solve for ( x ) where the second derivative equals zero or is undefined.

First derivative of ( f(x) = x^4 ): [ f'(x) = 4x^3 ]

Second derivative of ( f(x) = x^4 ): [ f''(x) = 12x^2 ]

Setting ( f''(x) ) equal to zero and solving for ( x ): [ 12x^2 = 0 ] [ x^2 = 0 ] [ x = 0 ]

So, the inflection point for ( f(x) = x^4 ) is 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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