For the function $f(x) = \frac{1}{x^2+2x+2}$

which of the following statements are TRUE?

A. $f(x)$ is increasing on $(-\infty, -1)$

B. $f(x)$ is decreasing on $(-\infty, -1)$

C. $f(x)$ is decreasing on $(-1, \infty)$

D. maximum value of $f(x)$ is 1

Choose the correct answer from the options given below:

Maximum slope of the curve $y = -x^3 + 3x^2 + 9x - 30$ is

The rate of change of volume of a sphere with respect to its surface area when radius of the sphere is 4 cm, is

The number of tangents to the curve $xy - 3y + 2 = 0$ having slope 2 is:

If the minimum value of $a$ is $-\frac{k}{2}$ such that the function $f(x) = x^2 + ax + 5$ is increasing in [1, 2]. Then value of $k$ is

Function $f(x) = x^3 - 3x + 3$ is

(A) Increasing in the interval $(-1, 1)$

(B) Increasing in the interval $(1, \infty)$

(C) Decreasing in the interval $(-1, 1)$

(D) Increasing in the interval $(-\infty, -1) \cup (1, \infty)$

Choose the correct answer from the options given below:

The maximum value of $f(x)=\dfrac{1}{3(x^2-x+1)}$ is :