Is #f(x)=-x^3-2x^2-3x-1# increasing or decreasing at #x=2#?

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Answer 1 · 2016-01-13T02:20:55

The function is decreasing.

The derivative of a function can tell us if the function is increasing or decreasing.

If #f'(2)>0#, then the function is increasing when #x=2#.
If #f'(2)<0#, then the function is decreasing when #x=2#.

To find #f'(x)#, use the power rule.

#f(x)=-x^3-2x^2-3x-1#
#f'(x)=-3x^2-4x-3#

Find #f'(2)#:

#f'(2)=-3(2^2)-4(2)-3=-23#

Since #-23<0#, the function is decreasing when #x=2#.

We can check a graph:

graph{-x^3-2x^2-3x-1 [-16.02, 16.02, -8.01, 8.01]}