Given a function $f(x) = ax + \frac{b}{x}$; $a > 0, b > 0$, then

Match List-I with List-II

List-I	List-II
(A) $f(x)$ has local maxima at $x$ is equal to	(I) $\sqrt{\frac{b}{a}}$
(B) $f(x)$ has local minima at $x$ is equal to	(II) $2\sqrt{ab}$
(C) Local Maxima of $f(x)$	(III) $-\sqrt{\frac{b}{a}}$
(D) Local Minima of $f(x)$	(IV) $-2\sqrt{ab}$

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If the interval in which f(x) = $\frac{x}{4}$ + $\frac{4}{x}$, x ≠ 0 is strictly increasing is (-∞, a) ∪ (b, ∞), then

The function $f(x) = 2\log_e(x-2) - x^2 + 4x + 1, (x > 2)$ is increasing on the interval:

For the function $f(x) = e^{-2x}(2-x)^2$, the point of local maxima is:

For the function $f(x) = e^x + e^{-x}$

(A) $f'(x) = e^x - e^{-x}$

(B) The critical point is $x = 0$

(C) The minimum value is 1

(D) $x = 0$ is the point of local minimum.

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Match List I with List II

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If $f(x) = (x+3)e^{-x}$, then which of the following statements are True?

(A) Function $f(x)$ is increasing on $(-2, \infty)$.

(B) Function $f(x)$ is decreasing on $(-2, \infty)$.

(C) Function $f(x)$ is increasing on $(-\infty, -2)$.

(D) Function $f(x)$ is decreasing on $(2, 3)$.