(Solutions based entirely on graphical or numerical methods are not acceptable.)
The power consumption of a high-performance computing cluster, P P\,P in kilowatts, is modeled by the function
P(t)=0.8t2.5−128t+2000,t>0 P(t) = 0.8t^{2.5} - 128t + 2000, \quad t > 0 P(t)=0.8t2.5−128t+2000,t>0where t t\,t is the time in hours since the start of a large-scale simulation.
Solve the equation P′(t)=0P'(t) = 0P′(t)=0.
Solve the equation P′′(t)=15P''(t) = 15P′′(t)=15.
