How do you find the critical numbers of f(x)=(x+1)^7-7x-2

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lemjay | High School Teacher | (Level 3) Senior Educator

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To determine the critical numbers,  we have to take the derivative of the function.

`f'(x)=7(x +1)^6 - 7 -0`

`f'(x) = 7(x+1)^6-7`

Then, set the derivative equal to zero.


To solve for the value of x, factor the right side.



Simplify the equation by dividing both sides by 7.


Then, set each factor equal to zero. And isolate the x.

For the first factor:






For the second factor:






Therefore, the critical numbers are `x=-2` and `x=0` .