f′(x)=x1+2bx+a f has extremevalues and differentiable ⇒f′(−1)=0⇒a−2b=1 f′(2)=0⇒a+4b=−21⇒a=21,b=−41 f′′(−1),f′′(2) are negative. f has local maxima at −1,2
JEE Main 2012 — Mathematics Calculus
Let a,b∈R be such that the function f given by f(x)=ln∣x∣+bx2+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=21 and b=4−1
Held on 30 Apr 2012 · Verified 6 Jul 2026.
Statement 1 is false, statement 2 is true
Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
Statement 1 is true, statement 2 is false
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