Q.22. If x=-1 and x=2 are extremepoints of f(x) = \alpha log x +\beta x^{2}+x , \alpha and \beta are constants, then the value of \alpha^2 + 2\beta is:
A. -3
B. 3
C.\frac{3}{2}
D.5
Answer:- B.3
Explanation :- According to the given condition,
f'(1) = 0 and f'(2) = 0
f(x) = α log x + βx2+x
f'(x)=\frac{\alpha }{x}+2\beta x+1f'(-1) = 0
α + 2 β =1—-(ii)
and f'(2) = 0
α+ 8β= -2 —(ii)
From (i) and (ii) we get
\beta =\frac{-1}{2\beta =\frac{-1}{2}} and α=2
α2 + 2β = 4-1 = 3