Mathematics
OpenStudy (anonymous):

Must critical points be real numbers?

OpenStudy (anonymous):

if you are working with real valued functions yes

OpenStudy (anonymous):

so for example if your function has derivative \[x^2+1\] it has no critical points

OpenStudy (anonymous):

wouldn't 0 be a critical point in that case?

OpenStudy (anonymous):

i meant that \[f'(x)=x^2+1\] so \[f(x)\] has no critical points

OpenStudy (anonymous):

oh sorry. missed that.

OpenStudy (anonymous):

clear now yes?

OpenStudy (anonymous):

when simplified, the derivative I have is equal to \[13x ^{2}+8x+12=0\]. So it would likewise have no critical points because the roots are complex. Correct?

OpenStudy (anonymous):

this has no zeros then it it always positive so your function is strictly increasing

OpenStudy (anonymous):

so yes. if the zeros are complex, no critical points

OpenStudy (anonymous):

Originally it had a factor of -4 so it was strictly decreasing, but yes. I see. I know that it has no extrema, but I was getting conflicting answers on whether it technically has critical points to define the intervals.

OpenStudy (anonymous):

Thank you.