# How do you determine whether the function #y=x^2 # is concave up or concave down and its intervals?

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To determine whether the function ( y = x^2 ) is concave up or concave down, you can examine its second derivative.

- Find the second derivative of the function ( y = x^2 ) with respect to ( x ).

[ \frac{{d^2y}}{{dx^2}} = 2 ]

- Since the second derivative is a constant (in this case, 2), you can conclude that the function ( y = x^2 ) is concave up everywhere.

Therefore, the function ( y = x^2 ) is concave up for all real numbers ( x ).

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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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