Expert: Steve Holleran - 8/8/2008

Question
Just asked you a question, and sorry I typed the equation wrong. It should read: x^5+x+7=0.

Answer
Hi Tim,

Okay, what the hint is probably referring to is that if you take a derivative:

                y=  x^5 + x + 7 --> y' = 5x^4 + 1

this derivative is never = 0, because 5x^4 is always positive or 0, so therefore the curve has no turning points.

Since its an odd function, and 5th degree, it can have 5, 3 or 1 real zeros, but it can't have 5 or 3, because then it would have turning points, so it must have only 1 real zero.

Steve