# How do you find the critical points for #f'(x)=11+30x+18x^2+2x^3#?

The critical numbers for

This is never undefined, so we need only find the zeros:

So, if you use "critical points" to mean points on the graph (rather than points in the domain), then they will be:

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To find the critical points for ( f'(x) = 11 + 30x + 18x^2 + 2x^3 ), we need to find the values of ( x ) where the derivative is equal to zero or undefined.

First, find the derivative of ( f'(x) ) which is ( f''(x) ).

Then, set ( f''(x) = 0 ) and solve for ( x ). These solutions will give you potential critical points.

Additionally, check for values of ( x ) where ( f''(x) ) is undefined, which could also indicate critical points.

After finding these potential critical points, you need to evaluate them to determine if they are indeed critical points by examining the behavior of the function ( f'(x) ) around those points.

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