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

α = -6, β = 1/2

α = -6, β = -1/2

α = 2, β = -1/2

α = 2, β = 1/2

Answer

α = 2, β = -1/2

Here, x =-1 and x = 2 are extreme points of f(x) = α log|x| +βx² +x then,
f'(x) = α/x +2βx + 1
f'(-1) = -α -2β +1 = 0 .... (i)
[At extreme point f'(x) = 0]
f'(2) = α/x +4βx + 1 = 0 .. (ii)
On solving Eqs (i) and (ii), we get
α = 2 and β = -1/2