How do you know a function is decreasing or increasing at #x=1# given the function #4x^29x#?
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To determine whether a function is increasing or decreasing at a particular point ( x = 1 ) given the function ( f(x) = 4x^2  9x ), you need to examine the sign of the derivative of the function at that point.

Find the derivative of the function ( f(x) ) with respect to ( x ) using the power rule: ( f'(x) = 8x  9 ).

Evaluate the derivative at ( x = 1 ): ( f'(1) = 8(1)  9 = 8  9 = 1 ).

If ( f'(1) > 0 ), the function is increasing at ( x = 1 ). If ( f'(1) < 0 ), the function is decreasing at ( x = 1 ).
Since ( f'(1) = 1 < 0 ), the function ( f(x) = 4x^2  9x ) is decreasing at ( x = 1 ).
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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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