Mathematics

Problem

The gross revenue

R(x)

(in thousand rupees) from selling

x

hundred gadgets is given by

R(x)=-2x^{3}+15x^{2}+60x,\qquad x\ge 0.

For which range of

x

is the revenue increasing? a)

x>\dfrac{5+\sqrt{65}}{2}

0<x<\dfrac{5+\sqrt{15}}{2}

0<x<\dfrac{5+\sqrt{65}}{2}

0\le x\le \dfrac{5+\sqrt{65}}{2}