If the area of an equilateral triangle is increasing at the rate of $4\sqrt{3}$ cm²/sec, then the rate of increase of its perimeter when the side is 4cm, is

The maximum value of the function $f(x)=\sin x(1+\cos x)$ in the internal $[0,\pi]$ is

The function $f(x) = x^3 + 3x^2 + 4x + 4$, $x \in \mathbb{R}$ (set of real numbers) :

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:

If $x = -1$ and $x = -2$ are the extreme points of $f(x) = \alpha\log|x| + \beta x^2 + x$ then

The function $f(x)=17-9x+6x^2-x^3$ is strictly increasing in the interval, is:

The function $f(x) = 4 - 3x + 3x^2 - x^3$ is (Here $\mathbb{R}$ is set of real numbers)