If the demand law is given by p = 10e^{\(-\frac { x }{ 2 } \)} then find the elasticity of demand.

Show that the function f(x) = x³ − 3x² + 4x, x \(\in\) R is strictly increasing function on R.

The profit function of a firm in producing x units of a product is given by\(p(x)=\frac { { x }^{ 3 } }{ 3 } +{ x }^{ 2 }+x\). Check whether the firm is running a profitable business or not. 

A tour operator charges Rupees 136 per passenger with a discount of 40 paisa for each passenger in excess of 100. The operator requires at least 100 passengers to operate the tour. Determine the number of passenger that will maximize the amount of money the tour operator receives.

Find out the elasticity of demand for the following functions
(i) p = xe^x
(ii) p = xe^-x
(iii) p = 10\({ e }^{ -\frac { x }{ 3 } }\)