# For what values of x is #f(x)= 2x^3-9x # concave or convex?

I try not to confuse myself over "concave" vs. "convex". Instead I think about it as concave up or concave down.

It is the second derivative at each of these points that tells you which of these three they are. Positive, if concave up, and negative, if concave down.

For us to find where the extrema are:

graph{2x^3 - 9x [-10,10, -10.14, 10.13]}

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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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