Find the points of local maxima and minima if any of the following function defined in $$0 \le x \le 6,$$ $$\,\,\,\,f\left( x \right) = {x^3} - 6{x^2} + 9x + 15.$$

If an instruction takes $${\rm I}$$ microseconds and a page fault takes an additional $$j$$ microseconds, the effective instruction time if on the average a page fault occurs every $$k$$ instruction is:

A computer has six tape drives, with n processes competing for them. Each process may need two drives. What is the maximum value of n for the system to be deadlock free?

In a resident $$–OS$$ computer, which of the following systems must reside in the main memory under all situations?