# Is #f(x)=-2x^5-2x^3+3x^2-x+3# concave or convex at #x=-1#?

Convex.

You can tell if a function is concave or convex by the sign of its second derivative:

To find the second derivative, apply the power rule to each term twice.

This mostly becomes a test of keeping track of your positives and negatives.

We can check the graph of the original function:

graph{-2x^5-2x^3+3x^2-x+3 [-2.5, 2, -30, 30]}

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The function f(x) = -2x^5 - 2x^3 + 3x^2 - x + 3 is concave at x = -1.

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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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- Is #f(x)=(x-3)(x-2)-x^2# concave or convex at #x=3#?

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