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.
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?
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