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Let a, b \in \mathbb{R} be such that the function f defined by f(x)=\ln|x|+bx^2+ax, for x\neq 0, has stationary extreme points at x=-1 and x=2. Statement-1: f has a local maximum at x=-1 and also at x=2. Statement-2: a=\tfrac12 and b=-\tfrac14
- Statement-1 is false, Statement-2 is true.
- Statement-1 is true, Statement-2 is true; Statement-2 correctly explains Statement-1.
- Statement-1 is true, Statement-2 is true; Statement-2 does not correctly explain Statement-1.
- Statement-1 is true, Statement-2 is false.
Correct answer: Statement-1 is true, Statement-2 is true; Statement-2 does not correctly explain Statement-1.
Solution
The function has stationary points at x=-1 and x=2, indicating potential local extrema. However, the specific values of a and b do not guarantee that both points are local maxima; further analysis of the second derivative is needed to confirm the nature of these extrema.
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