Is #f(x)=-2x^3-5x^2-6x-1# increasing or decreasing at #x=1#?
DECREASING
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To determine whether ( f(x) = -2x^3 - 5x^2 - 6x - 1 ) is increasing or decreasing at ( x = 1 ), we need to evaluate the sign of the derivative at that point.
The derivative of ( f(x) ) with respect to ( x ) is ( f'(x) = -6x^2 - 10x - 6 ).
Substitute ( x = 1 ) into the derivative:
[ f'(1) = -6(1)^2 - 10(1) - 6 = -6 - 10 - 6 = -22 ]
Since the derivative is negative at ( x = 1 ) (( f'(1) = -22 )), this indicates that the function is decreasing at ( x = 1 ).
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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.
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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