The function $f(x) = \frac{x}{3} + \frac{3}{x}$ is increasing in the interval:

Match List-I with List-II

The function $f(x) = (x - 1)(x + 1)^2$ has

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The maximum value of $2x^3 - 24x + 107$ in the interval $[1, 3]$ is :

The equation of the normal to the curve $y = x - \frac{1}{x}$ at $(1,0)$ is:

The function $f(x) = \frac{x - 2}{x + 1}, x \neq -1$ is increasing when (Where $\mathbb{R}$ is a set of real numbers)

$f(x)=\sin x+\frac{1}{2} \cos 2 x \text { in }\left[0, \frac{\pi}{2}\right]$

(A) $f^{\prime}(x)=\cos x-\sin 2 x$

(B) The critical points of the function are $x=\frac{\pi}{6}$ and $x=\frac{\pi}{2}$

(C) The minimum value of the function is $2$

(D) The maximum value of the function is $\frac{3}{4}$

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If $y = ax^2 + bx$ has minima at $x = 2$ and the minimum value is -12, then which of the following are correct?

(A) $a = 3$

(B) $a = -3$

(C) $b = 12$

(D) $b = -12$

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