If the total revenue function for a blender is R(x) = 58x − 0.01x2

Question

where x is the number of units sold, what is the average rate of change in revenue R(x) as x increases from 14 to 28 units?
$ per unit

Answer 1

The average rate of change for the blender as x changes from 14 to 28 cab be found by the following formula

 

ΔR = R(b)-R(a)/b-a , where b =28, and a =14 

 

Note that this formula constitutes the average slope of line between the two points with x coordinates of 14 and 28

 

R(b)=R(28) = 58(28)-0.01(28²) = 1616.2

 

R(a)=R(14) = 58(14)-0.01(14²) = 810.0

 

ΔR = (1612.3-810.0)/(28-14)= 57.3 is the average rate of change in $ per unit