Find the largest open interval where the function is changing as requested decreasing; f(x)=x^3-4x

to find the largest open interval where f is in decreasing, we find the first derivative, f'. then we find the critical numbers, aka where f'(x) = 0 or undefined. after that, we determine where f' is negative and positive using the critical numbers as region boundaries.so we first find the first derivative.

differentiate f using product rule:  

find where f'(x) = 0; set f'(x) = 0 and solve for x  

those two numbers are critical numbers. set up a sign chart and test the three intervals that form from these two critical numbers. these three intervals are  

evaluate f' at numbers in each interval to test the sign of f'. for example, in the interval , we can test f'(0) (since 0 is in that open interval) and that it is negative.

the only interval on which f is decreasing is    

and, therefore, that is the answer.

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step-by-step explanation:

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