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If x = −1 and x = 2 are extreme points of f(x) = α log |x| + βx² + x then:
- α = 2, β = 1/2
- α = −6, β = 1/2
- α = −6, β = −1/2
- α = 2, β = −1/2
Correct answer: α = 2, β = −1/2
Solution
The correct option indicates that the second derivative test for extreme points at x = -1 and x = 2 yields a positive result for concavity, which is satisfied by the values α = 2 and β = -1/2, ensuring that these points are indeed local minima or maxima.
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