Question

If \( x=-1 \) and \( x=2 \) are extreme points of \[ f(x) = \alpha \log|x| + \beta x^2 + x \quad (x \ne 0), \] then:

• A. \( \alpha = -6, \ \beta = \frac{1}{2} \)
• B. \( \alpha = -6, \ \beta = -\frac{1}{2} \)
• C. \( \alpha = 2, \ \beta = -\frac{1}{2} \)
• D. \( \alpha = 2, \ \beta = \frac{1}{2} \)

Hint:

For extrema problems: \begin{itemize} \item Set derivative zero at given points. \item Solve simultaneous equations. \end{itemize}

Answer 1

The Correct Option is A