Match List-I with List-II

List-I	List-II
(a) If $x = t^2$ and $y = t^3$, then $\frac{d^2y}{dx^2}$ at $t = 1$	(i) $-2$
(b) If $f(x) = \sqrt{x} + 1$, then $f''(1)$	(ii) $-1$
(c) The minimum value of $f(x) = 9x^2 + 12x + 2$ is	(iii) $\frac{3}{4}$
(d) The point of inflexion of the function $f(x) = (x-2)^4 (x+1)^3$ is	(iv) $-\frac{1}{4}$

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The interval in which the function $f(x) = -x^2 - 2x + 18$ is decreasing is :

The given function $f(x) = x^5 - 5x^4 + 5x^3 - 1$; has/have

(a) local maxima at $x = 1$

(b) local maximum value is 0

(c) local minimum at $x = 3$

(d) local minimum value is $-28$

(e) The point of inflexion is $x = 1$

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The total cost $c(x)$ associated with the production of $x$ units of an item is given by $c(x) = 0.001x^3 + 0.06x^2 + 20x + 500$. The marginal cost when 10 units are produced is:

If the maximum value of the function $f(x) = \frac{\log_ex}{x}$, $x > 0$ occurs at $x = a$, then $a^2f''(a)$ is equal to

Let $f(x)$ be a function defined by $f(x) = 2x^3 - 24x + 107$. If $\alpha$ and $\beta$ are the maximum and minimum values respectively in the interval $[1,3]$, then $\alpha-\beta$ is equal to:

If the function $f(x) = 2x^2 - kx + 7$, is increasing on $[1,2]$, then $k$ lies in the interval