defence exam Agniveer Vayu Group X & XY Mock Test 01/2026 Mathematics Differential Calculus Applications of Derivatives
Let \(a,b \in \mathbb{R}\) be such that the function \(f\) given by \(f(x)=\ln|x|+bx^{2}+ax, x \neq 0\) has extreme values at \(x=-1\) and \(x=2\).
Statement 1 : \(f\) has local maximum at \(x=-1\) and at \(x=2\)
Statement 2 : \(a=\dfrac{1}{2}\), \(b=\dfrac{-1}{4}\)
1
Statement 1 is false, Statement 2 is true
2
Statement 1 is true, Statement 2 is true; Statement 2 is correct explanation for Statement 1
3
Statement 1 is true, Statement 2 is true; Statement 2 is not a correct expalnation for Statement 1.
4
Statement 1 is true, Statement 2 is false.