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Given p(x)=x^4+ax^3+bx^2+cx+d,such that x=0 is the only real root of p'(x)=0.If p(-1)<p(1),then in the interval [-1,1],which is maximum and minimum of p(-1) and p(1)?:
a)p(-1) is minimum and p(1) is maximum.
b)p(-1) is not minimum and p(1) is maximum.
c)neither p(-1) is minimum nor p(1) is maximum.

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asked by Gunjan
  1. p'(x) = 4x^3 + 3ax^2 + 2bx + c
    since p'(0) = 0, c=0 and
    p'(x) = x(4x^2+3ax+2b)
    Since p' has no other roots,
    9a^2-32b < 0
    a^2 < 32b/9

    p(-1) = -4+3a-2b+c
    p(1) = 4+3a+2b+c

    It appears that the answer is (c)

    Consider x^4+x^3+x^2
    min is at (0,0) max at (1,3)

    Consider x^4-x^3+x^2
    min is at (0,0) max at (-1,3)

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    posted by Steve

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