# How do you find points of inflection of the function function #h(x) = −x^4 + x^2 − 1#?

Finding the zeros of the second derivative and determining whether its sign changes at those points is necessary to compute the points of inflection.

Verifying whether the derivative's sign changes

graph{-12x^2+2 [-2.252, 2.254, 4.506, 4.505]}

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To find the points of inflection of the function ( h(x) = -x^4 + x^2 - 1 ), we first find its second derivative, ( h''(x) ). Then, we solve ( h''(x) = 0 ) to find the x-values of potential inflection points. Finally, we test these x-values using the second derivative test to determine if they are points of inflection.

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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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