Find the x coordinate(s) of all the inflection points of f(x)=(1/20)x^5+(1/12)x^4+x+1?

Question

anonymous · Answer

a)0
b)1
c)-1
d)2
e)-2

anonymous · Answer

do you have the second derivative?

anonymous · Answer

$$x ^{3}+x ^{2}$$

anonymous · Answer

ok... factor out the gcf and set this second derivative to zero.  what are your solutions?

anonymous · Answer

x=0 and x=-1

anonymous · Answer

ok... notice that the factor x^2 has multiplicity of 2.  that means the first derivative is increasing from -1 to 0 but from 0 to inf it stays positive so again, the first derivative is increasing.  i.e., there was no sign change in the second derivative here.  therefore the graph does not have an inflection point here at x = 0.

but @ x=-1, there is a sign change... this is an inflection point.

anonymous · Answer

I'm going to have to read that several times but thank you!

anonymous · Answer

yw...:)

anonymous · Answer

i think i may have to read it more than once myself!   :)