Originally Posted by
misiaizeska The polynomial function is: f(x) = x(x-4)^3
I know that you have to find the first derivative of the function, which is:
f'(x): 4x^3 - 36x^2 + 96x - 64
f'(x): x^3 - 9x^2 + 24x - 16 No! You can not just throw away common factors. The only reason you would normally be able to do this is if you have set the equation equal to 0, which you have NOT done yet!
We are supposed to set f'(x)=0, so:
x^3 - 9x^2 + 24x - 16 = 0 This is correct NOW.
I would think that you bring the "-16" to the other side: No! Polynomials can only be solved by factorising and using the Null Factor Law!
x^3 - 9x^2 + 24x = 16
Factor out the x:
x(x^2 - 9x + 24) = 16
But I know that 16 is not one of the critical numbers, so I'm not sure of where I went wrong. If anyone could correct me or provide suggestions, that would be very helpful! Thank you in advance!