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)?:

Question

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.

Answer 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)