grade 12 AP calculus
posted by Alannah on .
for f(x= -1/4x4-1/3x3+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?