Non-rigorous argument:Originally Posted bynath_quam

Consider the related function:

pp(x)=(1-eps-x)x(1+eps-x)(x-3).

for any small eps>0. This has three roots all close to x=1, and in some

appropriate sense the average slope between x=1-eps and x=1+eps

is zero, so as eps goes to zero we generate a family of curves all of which

have an "average" slope of 0 near x=1, so it is reasonable to expect that

the slope of p(x) is 0 at x=1.

(I think I would need Roll's theorem (and the nested interval theorem?) to

make this rigorous, and your teacher would almost certainly forbid THAT).

RonL