# Is #f(x)=-3x^3-2x^2-12x-4# concave or convex at #x=-1#?

Convex.

It is concave if the second derivative is less than zero and convex if the second derivative is greater than zero.

The first derivative is:

The second derivative is: -18x – 4 At x = -1 this is 14, so the original equation is convex at that point.

Weisstein, Eric W. "First Derivative Test." From MathWorld--A Wolfram Web Resource. https://tutor.hix.ai

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To determine concavity, evaluate the second derivative of the function at the given point. [ f(x) = -3x^3 - 2x^2 - 12x - 4 ] [ f''(x) = -18x - 4 ] [ f''(-1) = -18(-1) - 4 = 18 - 4 = 14 ]

Since ( f''(-1) > 0 ), the function is concave upwards 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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