Home > Calculus > Interpreting the Sign of the First Derivative (Increasing and Decreasing Functions)

Is #f(x)=-2x^2-2x-1# increasing or decreasing at #x=-1#?

Answer 1

Scarlett Allison

It is increasing at #x=-1#.

#color(white)(xx)f(x)=-2x^2-2x-1#

#=>f'(x)=-4x-2# #=>f'(-1)=4-2# #color(white)(xxxxxxxx)=2#

#=>f'(-1)>0#

Therefore #f(x)# is increasing at #x=-1#. graph{-2x^2-2x-1 [-10, 10, -5, 5]}

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Answer 2

Axel Alvarez

To determine if ( f(x) = -2x^2 - 2x - 1 ) is increasing or decreasing at ( x = -1 ), we need to evaluate the sign of the derivative of the function at that point.

The derivative of ( f(x) ) with respect to ( x ) is ( f'(x) = -4x - 2 ).

Evaluate ( f'(-1) ):

( f'(-1) = -4(-1) - 2 = 4 - 2 = 2 )

Since ( f'(-1) ) is positive, ( f(x) ) is increasing at ( x = -1 ).

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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.