Prove that the function f(x) = x^101 + x^51 + x + 1 has neither a local maximum nor a local minimum.
I can take the derivative: f'(x) = 101x^100 + 51x^50 + 1
But what then?
nona.m.nona wrote:...The -51+/-46.9 will always be negative, so I can't do the 50th root of it to get a number for x. So this means I can't get a zero, so there isn't a critical point, so there can't be a max or min, right?