# How do you determine whether the function #g(x)=-x^2+3x+4# is concave up or concave down?

Two methods:

Using calculus, to determine concavity, investigate the sign of the second derivative.

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To determine whether the function ( g(x) = -x^2 + 3x + 4 ) is concave up or concave down, you need to find its second derivative. If the second derivative is positive, the function is concave up; if it's negative, the function is concave down.

First, find the first derivative of ( g(x) ), then find its second derivative.

[ g'(x) = -2x + 3 ]

[ g''(x) = -2 ]

Since the second derivative ( g''(x) ) is a constant (-2), and it's negative, the function is concave down everywhere.

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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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