How do you determine the intervals for which the function is increasing or decreasing given #f(x)=-x^3-2x+1#?

1 Answer
Shwetank Mauria
Sep 18, 2017

#f(x)# is always decreasing function and in interval notation it is decreasing for #(-oo,oo)#

Explanation:

For the function #f(x)=-x^3-2x+1#, as #x->oo#, #f(x)->-oo# and as #x->-oo#, #f(x)->oo#

As #(df)/(dx)=f'(x)=-3x^2-2# and as #x^2# is always positive,

#f'(x)# is always negative and hence

#f(x)# is always decreasing function and in interval notation it is decreasing for #(-oo,oo)#

graph{-x^3-2x+1 [-40, 40, -20, 20]}

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