The function $$f(x)=4 \sin ^3 x-6 \sin ^2 x +12 \sin x+100$$ is strictly

The cost and revenue functions of a product are given by $$c(x)=20 x+4000$$ and $$R(x)=60 x+2000$$ respectively, where $$\mathrm{x}$$ is the number of items produced and sold. The value of $$x$$ to earn profit is

A particle starts form rest and its angular displacement (in radians) is given by $$\theta=\frac{t^2}{20}+\frac{t}{5}$$. If the angular velocity at the end of $$t=4$$ is $$k$$, then the value of $$5 k$$ is

The function $$f(x)=x^2-2 x$$ is strictly decreasing in the interval