Problem

Problem

Let a,b∈Ra, b \in R be such that the function ff given byf(x)=log⁡∣x∣+bx2+ax,x≠0 has extreme values at x=−1 and x=2.f(x) = \log|x| + bx^2 + ax, x \neq 0 \text{ has extreme values at } x = -1 \text{ and } x = 2. Statement I ff has local maximum at x=−1x = -1 and at x=2x = 2 Statement II a=12 and b=−14[2012 AIEEE]a = \frac{1}{2} \text{ and } b = \frac{-1}{4} \quad [2012 \text{ AIEEE}] a. Statement I is false, Statement II is true b. Statement I is true, Statement II is true; Statement II is a correct explanation of Statement I c. Statement I is true, Statement II is true; Statement II is not a correct explanation of Statement I d. Statement I is true, Statement II is false

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