Okay.. so I've been doing calculus for about 4 hours at this point. And I haven't the slightest clue how to go about this proof... and my brain feels like jello.

Prove that the function

$\displaystyle f(x)=x^{101}+x^{51}+x+1$

has neither a local maximum nor a local minimum.

I took the derivative and now do not have any clue of what I need to do... how can I find critical points for it? Please help.

$\displaystyle f'(x)=101x^{100}+51x^{50}+1$