Math Help - Critical Points

1. Critical Points

say we have a polynomial function

$x^4+ux^2 + v x$ (u,v some numbers)

does anyone know why adding a higher order term to this will not change what happens near zero (in terms of critical points near zero)

2. Originally Posted by slevvio
say we have a polynomial function

$x^4+ux^2 + v x$ (u,v some numbers)

does anyone know why adding a higher order term to this will not change what happens near zero (in terms of critical points near zero)
If the function had an $x^5$ term, the derivative of that is $5x^4.$

For very small values of x, $5x^4$ will be very small... $5(0.1)^4=0.0005$

hence there will be only very small changes in the derivative near x=0, if a higher-power term is added to the function
(depending on the proximity of x to zero).