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

Answer 1

Two methods:

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

#g(x) = -x^2+3x+4#
#g'(x) = -2x+3#
#g''(x) = -2#
Since #g''(x)# is always negative, the graph of #g# is concave down on the domain of #g#. Which is to say: #g# is concave down on #(-oo, oo)#.
Using algebra, the graph of this quadratic is a parabola. Since the coefficient of #x^2# is negative, the parabola opens downward. It is concave down.
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Answer 2

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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Answer from HIX Tutor

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.

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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