For the function $f(x) = 3x^4 + 4x^3 - 12x^2 + 12$, then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$x = 0$	I.	Local minimum value of $f(x)$
B.	$x = -2$	II.	Local maximum of value of $f(x)$
C.	$f(0)$	III.	Point of local minima
D.	$f(1)$	IV.	Point of local maxima

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The length of a rectangle is decreasing at the rate of 4 cm/minute and the width is increasing at the rate of 3 cm/minute, then the rate of change of the perimeter is

For the function $f(x) = x^x, x > 0$, which of the following are TRUE?

(A) $f'(x) = x^x(1 + \log x)$

(B) $x = e$ is the critical point

(C) $f$ is increasing in $(\frac{1}{e}, \infty)$

(D) $f$ is increasing in $(0, \infty)$

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A particle moves along a curve $3y^2 = 6x^3 + 8$ such that its y-coordinate is changing at the rate of 9 cm/sec at point (1,2). Then the rate of a change of x-coordinate at the same point is :

If $x$ is real, the minimum value of $x^2 - 8x + 20$ is

The equation of the tangent, to the curve $y = x^2 - 2x - 3$ which is perpendicular to the line $x + 2y + 3 = 0$, is

The largest open interval, in which the function $f(x) = \frac{x}{x^2 + 1}$ increases, is