The revenue function for the given marginal revenue function
R'(x) = 0.06x² - 0.05x + 138 be
R(x) = 0.02x³ - 0.025x² + 138x
Given, a marginal revenue function,
R'(x) = 0.06x² - 0.05x + 138
we have to find the demand function
as, we know that the demand function can be find by integrating the marginal revenue function with respect to the variable x.
So, as the marginal revenue function is given,
R'(x) = 0.06x² - 0.05x + 138
On integrating with respect to x, we get
R(x) = 0.06x³/3 - 0.05x²/2 + 138x + C
where C is an arbitrary constant.
Also, it is given that
R(0) = 0
So, R(0) = 0.06(0) - 0.05(0) + 138(0) + C
0 = C
R(x) = 0.06x³/3 - 0.05x²/2 + 138x + 0
R(x) = 0.02x³ - 0.025x² + 138x
So, the revenue function be R(x) = 0.02x³ - 0.025x² + 138x
Hence, the revenue function be R(x) = 0.02x³ - 0.025x² + 138x
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