The gross revenue (in thousand rupees) from selling hundred gadgets is given by…

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

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}

(b)

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

(c)

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

(d)

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