# How do you determine the concavity for #f(x) = x^4 − 32x^2 + 6#?

The concavity of a function is the sign of its second derivative. If, in a set, it is positive, than the concavity is up, if negative the concavity is down, if it is zero, there could be an inflection point there.

So:

than

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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.

- For what values of x is #f(x)=4/x^2+1# concave or convex?
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- What are the inflections points of #y= e^(2x) - e^x #?
- Is the function concave up or down if #f(x)= (lnx)^2#?
- How do you find the first and second derivative of #(lnx)^3#?

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