What are the critical points of #f(x) = -3x^4 + 12x^3 + 6#?

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Answer 1 · 2016-07-04T13:41:09

#x = 0# an inflexion

#x=3# a max

#f(x) = -3x^4 + 12x^3 + 6#

#f'(x) = -12x^3 + 36x^2 = 12x^2(3-x)#

#f'' (x)= -36x^2 +72x = 36x(2-x) #

#f' = 0 \implies x = 0, 3#

#f''(0) = 0# ie an inflexion

#f''(3) = -108# ie a max