The function \(f(x)=x^{2}-4x+6\) is increasing in the interval

(a) The median of an equilateral triangle is increasing at the rate of 2√3 cm/s. Find the rate at which its side is increasing. OR (b) Sum of two numbers is 5. If the sum of the cubes of these numbers is least, then find the sum of the squares of these numbers.

Absolute minimum value of $f(x)=(x-2)^{2}+5$ in the interval [-3, 2] is :

A room freshner bottle in the shape of an inverted cone sprays the perfume at regular intervals such that volume of the perfume in the bottle decreases at the steady rate of 1 mm3/min. Find the rate at which level of perfume is dropping at an instant when level of perfume in the bottle is 10 mm, if the semi-vertical angle of conical bottle is $\frac{\pi}{6}$

Find the values of x for which $f(x)=x^{x}$, $x>0$ is increasing.