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Let a, b ∈ R be such that the function f defined by f(x)=ln|x|+bx²+ax, for x≠ 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=(1)/(2) and b=-(1)/(4)
- 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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