Let $f(x) = 1 - \sqrt{x^2}$, where the square root is to be taken as positive. Then:

The maximum value of $\sin x(1 + \cos x)$ occurs at

If the function $f(x) = x^3 - 3(a - 2)x^2 + 3ax + 7$,for some $a \in R$,is increasing in $(0, 1]$ and decreasing in $[1, 5)$,then a root of the equation $\frac{f(x) - 14}{(x - 1)^2} = 0$ $(x \neq 1)$ is

The difference between the absolute maximum and absolute minimum values of the function $f(x)=2x^3-15x^2+36x-30$ on the interval $[-1, 4]$ is:

If $y=a \log x+b x^2+x$ has its extremum values at $x=-1$ and $x=2$,then

Find the maximum and the minimum values,if any,of the function $f$ given by $f(x) = x^{2}, x \in R$.