Does every nth degree polynomial have (n-1) critical numbers? Why or why not?

Question

anonymous · Answer

nth degree polynomial has the form Pn(x)=a0+a1x+......+a(subscript n)x^n
coefficient can differ in number from 1 to n...
with a(subscript n) never equal to zero

anonymous · Answer

so, why ids it false?

anonymous · Answer

*is

sirm3d · Answer

a big NO! $$\large y=x^3+3x$$has no critical number

anonymous · Answer

can u give me another example besides that

sirm3d · Answer

$$\large y =x^5 + 5x$$

anonymous · Answer

stgreen, is that true?

sirm3d · Answer

why don't you test it yourself. take the derivative of the function, then try to find the real roots or critical numbers.

anonymous · Answer

okay

anonymous · Answer

ur right!

anonymous · Answer

but can u give me a really good explanation on why its false?

anonymous · Answer

nvrm.......how bout this: does an nth degree polynomial has at most (n-1) critical numbers

sirm3d · Answer

some derivatives, particularly quadratic polynomials, have no real roots, and we say the function has no critical number.

anonymous · Answer

okay thnx guys

sirm3d · Answer

at most (n-1) critical numbers allow 0, 1, 2, 3, .. up to (n - 1) critical numbers. This is certainly true.

anonymous · Answer

ya...i got that one