Asked by Britt
Ralph is taking his final exam. After t minutes into the exam Ralph has correctly solved P(t)=-.001t^3+.078t^2+.16t problems.
a) at what time was Ralph solving problems most efficiently?
b) at what time did Ralph's efficiency decline?
a) at what time was Ralph solving problems most efficiently?
b) at what time did Ralph's efficiency decline?
Answers
Answered by
Damon
dP/dt is how many problems he solves per minute
the maximum of dP/dt is where he is most efficient
I assume that after he is most efficient, he gets less efficient.
now
speed = v = dP/dt = -.003t^2+ .156 t +.16
dv/dt = 0 for max or min
0 = -.006t + .156
t = 26 for max or min efficiency
Now is it max or min or neurtral?
If the next derivative is negative, we were at a maximum
the next derivative is -.006
so indeed we have a maximum at t = 26, and it is all downhill from there.
the maximum of dP/dt is where he is most efficient
I assume that after he is most efficient, he gets less efficient.
now
speed = v = dP/dt = -.003t^2+ .156 t +.16
dv/dt = 0 for max or min
0 = -.006t + .156
t = 26 for max or min efficiency
Now is it max or min or neurtral?
If the next derivative is negative, we were at a maximum
the next derivative is -.006
so indeed we have a maximum at t = 26, and it is all downhill from there.
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