Answer:
- MR(29) = 194
- v(t) = 24t² -96t -120; v=0 at t = -1 and t = 5; a(t) = 48t -96
Explanation:
You want R'(29) for R(q) = -7q² +600q, and you want the velocity and acceleration functions for particle motion defined by s(t) = 8t³ -48t² -120t, along with times the velocity is zero.
1. Marginal revenue
The marginal revenue is the derivative of the revenue function.
R'(q) = -14q +600
R'(29) = -14·29 +600 = 194
The marginal revenue MR(29) = 194 dollars per unit.
2. Particle Motion
a. Velocity
The velocity function is the derivative of the position function:
s'(t) = v(t) = 24t² -96t -120
b. Stationary
The velocity is 0 when ...
0 = 24t² -96t -120 = 24(t² -4t -5) = 24(t +1)(t -5)
The factors are 0, so velocity is zero at ...
t = -1 and t = 5
c. Acceleration
The acceleration function is the derivative of the velocity function:
v'(t) = a(t) = 48t -96
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