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

grade 12 AP calculus 
Steve,
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 
grade 12 AP calculus 
Alannah,
how did you factor y' for this question?