Application of Derivatives · Mathematics · Class 12

The derivative of $$x^{2 x}$$ w.r.t. $$x$$ is:

The interval in which the function $$f(x)=2 x^3+9 x^2 +12 x-1$$ is decreasing is :

(a) The median of an equilateral triangle is increasing at the rate of $$2 \sqrt{3} \mathrm{~cm} / \mathrm{s}$$. 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.