For $x > 0$, the minimum value of $\frac{x}{\log_e x}$ is

The function $f(x) = x^2 - 4x + 6$ is

(A) Strictly decreasing on $(-\infty, 2) \cup (2, \infty)$

(B) Strictly increasing on $(2, \infty)$

(C) Strictly increasing on $(-\infty, \infty)$

(D) Strictly decreasing on $(-\infty, 2)$

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

Match List-I with List-II

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A square board of side 36cm is made into a box without top by cutting a square from each corner and folding up the flaps to form a box then maximum volume of the box is

The total cost $C(x)$ in Rupees associated with the production of $x$ units of an item is given by $C(x) = 0.007x^3 + 26x^2 + 15x + 400$. The marginal cost when 10 items are produced is:

The function $f(x) = 2x^3-15x^2+36x+4$ has local maxima at $x=$

If an open box with a square base is to be made out of a given card board of area $K^2$ square units, then the maximum volume of the box is