Question

The real valued function \( f(x) = \frac{x^2}{2} - \log(x^2+x+1) \) is

• A. Strictly decreasing in (1, \(\infty\))
• B. Strictly increasing in (1, \(\infty\))
• C. Strictly increasing in (-\(\infty\), 0)
• D. Strictly decreasing in (0, \(\infty\))

Hint:

To find intervals of increase/decrease for a function \(f(x)\), find the derivative \(f'(x)\) and determine its sign. The function is increasing where \(f'(x)>0\) and decreasing where \(f'(x)<0\). The critical points where the sign might change are where \(f'(x)=0\) or \(f'(x)\) is undefined.

Answer 1

The Correct Option is B