grade 12 AP calculus
posted by Alannah on .
for f(x= 1/4x41/3x3+2x, use analytic method to find the exact intervals on which the function is a)increasing, b)decreasing, c)concave up, d)concave down, then find any e)local extreme values, f)inflection points

y = 1/4 x^4  1/3 x^3 + 2x
y' = x^3  x^2 + 2
y'' = 3x^2  2x
inflection where y''=0: x=0, 2/3
local extrema where y'=0 and y''≠0: x=1
increasing where y'>0: x<1
decreasing where y'<0: x>1
concave up where y''>0: 2/3 < x < 0
concave down elsewhere 
how did you factor y' for this question?