How do you determine the intervals where #f(x)=x^24x+7# is concave up or down?
See below.
Answer 1
Answer 2
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To determine the intervals where ( f(x) = x^2  4x + 7 ) is concave up or down, you need to find the second derivative of the function and then analyze its sign.

Find the first derivative of ( f(x) ): [ f'(x) = 2x  4 ]

Find the second derivative of ( f(x) ): [ f''(x) = 2 ]

Since the second derivative is a constant ( 2 ), it is always positive. Therefore, the function ( f(x) ) is concave up for all real numbers ( x ).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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