Posted by Alannah on Monday, December 3, 2012 at 11:33am.
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, Monday, December 3, 2012 at 12:21pm
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, Tuesday, December 4, 2012 at 11:02pm
how did you factor y' for this question?
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