The largest interval, in which the function $f(x) = x^3 + 2x^2 - 1$ is increasing, is:

The points on the ellipse $4x^2 + y^2 = 4$ that are farthest from the point (1,0) are;

For the function $f(x) = \frac{x^4}{4} - 2x^3 + \frac{11}{2}x^2 - 6x$, which of the following statements are TRUE?

(A) Critical points of $f(x)$ are $x = 1, 2$ and $3$.

(B) $f(x)$ is increasing over $(1,2)$.

(C) $f(x)$ is decreasing over $(2,3)$.

(D) $f(x)$ is increasing over $(3,\infty)$.

Choose the correct answer from the options given below:

The slope of the normal to the curve $y = 2x^2 - 4$ at P (1, -2) is :

The minimum value of $f(x) = |2x - 1|$ is

The interval in which the $f(x) = \sin x - \cos x$, $0 \leq x \leq 2\pi$ is strictly decreasing is :

The function $f(x) = 3x + \cos 3x$ is (where R is set of real numbers)