How do you find the inflection points of #f(x)=x^530x^3#?
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To find the inflection points of ( f(x) = x^5  30x^3 ), we need to determine where the concavity changes.

Find the second derivative of ( f(x) ): ( f''(x) = \frac{d^2}{dx^2}(x^5  30x^3) ).

Set ( f''(x) = 0 ) and solve for ( x ) to find the points where the concavity may change.

Once you have the values of ( x ) where ( f''(x) = 0 ) or ( f''(x) ) is undefined, plug those values into the first derivative ( f'(x) ) to determine the concavity at those points.

Confirm the concavity changes by checking the signs of ( f''(x) ) around these points.

The points where the concavity changes are the inflection points.
So, in this case, you would find ( f''(x) ) and then solve ( f''(x) = 0 ) to identify the potential inflection points. After that, you would use the first derivative test to confirm the concavity changes and determine the inflection points.
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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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