If y=1+1/x, show that y is a strictly decreasing function for all real values of x(x\(\neq\)0).

Prove that 75-12x+6x²-x³ always decreases as x increases.

Find the maximum and minimum values of x³-6x²+7

A certain manufacturing concern has the toal cost function C = \({1\over5}x^2-6x+100\).Find when the tatal cost is minimum.

A manufacturer has to supply 12,000 units of a product per year to his customer. The demand is fixed and known and no shortages are allowed. The inventory holding cost is 20 paise per unit per month and the set up cost per run is Rs.350. Determine (i) the optimum run size q₀. (ii) Optimum scheduling period t₀ (iii) minimum total variable yearly cost.