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Question:

If x = -1/2 and x = 2 are extreme points of f(x) = αlog|x| + βx² + x, then α = ?, β = ?

α = -6, β = 1/2

α = 2, β = 12

α = 2, β = 1/2

α = -6, β = 12

Solution:

f'(x) = α/x + 2βx + 1
α/x + 2βx + 1 = 0 has roots -1/2 and 2
Putting x = -1/2, -2β + α = 1
Putting x = 2, 4β + α = -1
Solving the above equations, we get α = 2, β = -1/2
Ans is Option: [C]