Homework SourseFind the intervals on which the graph of f is concave upward
Find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the inflection points.
f(x)=-x^6+12x^5-12x+5
f(x)=-x^6+12x^5-12x+5
Solution
f\'(x)=-6x^5+60x^4-12 f\'\'(x)=-30x^4+240x^3 so for f\'\'(x)=0 we have x^3(-30x+240)=0 i.e x=0 and x=8 where 0 will have multipicity of 3 in the solution so 0 and are inflexion points and we have three intervals I1=(-infinity,0)=concave down I2=(0,8)=concave upward I3=(8,infinity)=concave down
