For what values of x is #f(x)=-2x^2-6x+4# concave or convex?

Answer 1

Aurora Alvarado

The function is concave everywhere.

Algebra

The graph is a parabola that opens downward. So it is concave.

Calculus

#f'(x) = -4x-6#

#f''(x) = -4#

Since #f''(x)# is negative for all #x#, the function is concave for all #x#.

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Answer 2

Elijah Abram

To determine where the function ( f(x) = -2x^2 - 6x + 4 ) is concave or convex, we need to find the second derivative of the function and then examine its sign.

First, find the first derivative of ( f(x) ): [ f'(x) = -4x - 6 ]

Now, find the second derivative of ( f(x) ): [ f''(x) = -4 ]

Since the second derivative is a constant (-4), it is negative for all real values of ( x ). This means that the function is concave down for all values of ( x ), and there are no values for which it is convex.

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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.