How do you find the inflection points for the function #f(x)=x^3+x#?
By taking derivatives,
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To find the inflection points for the function (f(x) = x^3 + x), we need to find the points where the concavity changes. Inflection points occur where the second derivative changes sign or where the second derivative is zero.

Find the first derivative of (f(x)): [f'(x) = 3x^2 + 1]

Find the second derivative of (f(x)): [f''(x) = 6x]

Set (f''(x) = 0) to find possible inflection points: [6x = 0] [x = 0]

Test the sign of (f''(x)) around (x = 0):
 For (x < 0), (f''(x) < 0), so the concavity is downward.
 For (x > 0), (f''(x) > 0), so the concavity is upward.
Therefore, the function (f(x) = x^3 + x) has an inflection point at (x = 0).
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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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