In a high-pressure experimental chamber, the relationship between Temperature, TTT, and Pressure, PPP, is modeled by the implicit equation:
T2−10T=2P2−16P+5 T^2 - 10T = 2P^2 - 16P + 5 T2−10T=2P2−16P+5Find an expression for dTdP\frac{dT}{dP}dPdT in terms of TTT and PPP.
The model predicts that temperature TTT has no real solutions for pressure values in the interval (p,q)(p, q)(p,q). Use your result from part (a) or otherwise to determine the value of ppp and the value of qqq.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change, matched to the Edexcel A Level Maths (9MA0) 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.
