Given P(x) = x⁴ + a x³ + b x² + 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 ]:

(A) P(-1) is not minimum but P(1) is the maximum of P

(B) P(-1) is the minimum but P(1) is not the maximum of P

(C) Neither P(-1) is the minimum nor P(1) is the maximum of P

(D) P(-1) is the minimum and P(1) is the maximum of P

Limit, Continuity and Differentiability: JEE Main 2009 Mathematics question

JEE Main 2009 · Annual, Paper 1 · Q2625

JEE Main 2009Annual, Paper 1MathematicsHardLimit, Continuity and Differentiability420× since 2002

Given

P\left( x \right) = {x^4} + a{x^3} + b{x^2} + cx + d

such that

x=0

is the only real root of

P'\,\left( x \right) = 0.

P\left( { - 1} \right) < P\left( 1 \right),

then in the interval

\left[ { - 1,1} \right]: