If the revenue function is $R ( x ) = x ^ { 2 / 3 } + 2 x ^ { 1 / 2 } + 6 x + 2$ for producing a product, find the marginal revenue at a production level of 10 units.
A) $\frac { 2 } { 3 }$ $( 10 ) ^ { - 1 / 3 }$ + $( 10 ) ^ { - 1 / 2 }$ + 6
B) $\frac { 2 } { 3 }$ $( 10 ) ^ { - 1 / 3 }$ + $4 ( 10 ) ^ { - 1 / 2 }$ + 6
C) $( 10 ) ^ { 2 / 3 }$ + 2 $\text { (10) } 1 / 2$ + 6(10) + 2
D) $\frac { 2 } { 3 }$ $( 10 ) ^ { - 1 / 3 }$ + $( 10 ) ^ { 1 / 2 }$ + 6
E) $\frac { 2 } { 3 }$ $( 10 ) ^ { 1 / 3 }$ + $( 10 ) ^ { 1 / 2 }$ + 6

Question

Quizplus · Accepted Answer

The marginal revenue is the derivative of the revenue function. So, we have:$$R'(x) = \frac{d}{dx}(x^{2/3} + 2x^{1/2} + 6x + 2) = \frac{2}{3}x^{-1/3} + x^{-1/2} + 6$$At a production level of 10 units, the marginal revenue is:$$R'(10) = \frac{2}{3}(10)^{-1/3} + (10)^{-1/2} + 6 = \frac{2}{3}(0.215) + 0.316 + 6 = 6.231$$

If the Revenue Function Is R(x)=x2/3+2x1/2+6x+2R ( x ) = x ^ { 2 / 3 } + 2 x ^ { 1 / 2 } + 6 x + 2R(x)=x2/3+2x1/2+6x+2

If the Revenue Function Is $R ( x ) = x ^ { 2 / 3 } + 2 x ^ { 1 / 2 } + 6 x + 2$