The marginal revenue (in thousands of dollars) from the sale of x gadgets is given by the following function. upper r prime(x)equals4x(x squared plus 26 comma 000 ) superscript negative two thirds a. find the total revenue function if the revenue from 120 gadgets is $25 comma 879. b. how many gadgets must be sold for a revenue of at least $45,000?

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step-by-step explanation:

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)