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

The point on the curve y = (x - 2)² at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4) is:

The point of local maxima of the function $f(x) = (x - 2)^5(x + 2)^2$ is

Match List-I with List-II

Choose the correct answer from the options given below:

If the local maximum value of the function $f(x)=x^3-2\lambda x^2+\lambda^2 x, \lambda>0$ is 108, Then the local minimum value of the function occurs at

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 $f(x) = \sin x - \cos x$, $x \in [0, 2\pi]$ then

(A) $f(x)$ is increasing in $(0, \frac{3\pi}{4})$

(B) $f(x)$ is decreasing in $(0, \frac{3\pi}{4})$

(C) $f(x)$ is decreasing in $(\frac{3\pi}{4}, \frac{7\pi}{4})$

(D) $f(x)$ is decreasing in $(\frac{7\pi}{4}, 2\pi)$

Choose the correct answer from the options given below: