(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.
Practise AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
