If $\alpha$ and $\beta$ are absolute maximum and absolute minimum values of a function $f(x)=\dfrac{x}{2}+\dfrac{2}{x}$ on the interval $[1,2]$, then the value of $\alpha+\beta$ is:

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:

The rate of change (in $\mathrm{cm}^{2} / \mathrm{s}$ ) of the total surface area of a hemisphere with respect to radius $r$ at $r=\sqrt[3]{1.331} \mathrm{~cm}$ is :

In which of the following interval the function $f(x) = x^x, x > 0$ is strictly increasing?

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

Angle between tangents to the curve $y = x^2 - 5x + 6$ at the points (2, 0) and (3, 0) is :

The side of an equilateral triangle is increasing at the rate of 2 cm/sec. The rate at which the area of the triangle is increasing, when the side of the triangle is 5 cm, is