Let a,b R be such that the function f given by f(x) = In| x | + b x² + ax, x ≠ 0 has extreme values at x=-1 and x=2 Statement-1: f has local maximum at x=-1 and at x=2. Statement-2: a = 1/2 and b = (-1)/4

(B) Statement - 1 is true, Statement - 2 is true; Statement - 2 is a correct explanation for Statement - 1.

(A) Statement - 1 is false, Statement - 2 is true.

(C) Statement - 1 is true, Statement - 2 is true; Statement - 2 is not a correct explanation for Statement - 1.

(D) Statement - 1 is true, Statement - 2 is false.

Limit, Continuity and Differentiability: JEE Main 2012 Mathematics question

JEE Main 2012 · Annual, Paper 1 · Q2629

JEE Main 2012Annual, Paper 1MathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

a,b \in R

be such that the function

f

given by

f\left( x \right) = In\left| x \right| + b{x^2} + ax,\,x \ne 0

has extreme values at

x=-1

and

x=2

Statement-1 :

f

has local maximum at

x=-1

and at

x=2

. Statement-2 :

a = {1 \over 2}

and

b = {-1 \over 4}