consider PV =nRT , P,V,T = pressure , volume , temperature respectively. nR = constant

let n=R=1

differentiate with respect to t

dP/dt = ∂P/∂T * dT/dt + ∂P/∂V * dV/dt......................∂P/∂T = 1/V , ∂P/∂V = -T/V^{2}

considering an experiment where i can adjust the rate dV/dt and dT/dt as i want

1. find V(t) and T(t) that give maximum dP/dt at point V=10 cm^{3}, T = 25 degree

2. find V(t) and T(t) that give maximum dP/dt at point V=V_{0}cm^{3}, T = T_{0}degree