What are the points of inflection, if any, of #f(x)= (x-3)/sqrt(x^5-x^3-3x+4) #?

Answer 1

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Answer 2

To find the points of inflection, we first need to find the second derivative of the function and then determine where it equals zero. After that, we can check the concavity of the function around those points.

The second derivative of f(x) is: f''(x) = (24x^4 - 2x^2 - 10) / (2(x^5 - x^3 - 3x + 4)^(5/2)) - (15(x - 3)(3x^4 - 2x^2 - 3)) / (2(x^5 - x^3 - 3x + 4)^(7/2))

Points of inflection occur where the second derivative changes sign. Therefore, we need to find where f''(x) = 0 and then test the concavity around those points.

However, the expression for the second derivative is quite complex, and finding its roots analytically might be challenging. We can use numerical methods or software to approximate the points of inflection.

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Answer from HIX Tutor

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.

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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