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

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Answer 1 · 2017-09-18T08:52:51

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

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]}

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