The relationship between the pressure ppp and temperature ttt of a specific gas model is described by the equation
p3t+2pt3=12 p^3t + 2pt^3 = 12 p3t+2pt3=12Prove that the curve representing this relationship does not intersect the coordinate axes in the ppp-ttt plane.
Show that
dtdp=−3p2t+2t3p3+6pt2 \frac{dt}{dp} = -\frac{3p^2t + 2t^3}{p^3 + 6pt^2} dpdt=−p3+6pt23p2t+2t3Prove that the model has no stationary points.
In the case when p>0p > 0p>0, find the equation of the tangent line to the curve at the point where t=1t = 1t=1. Give your answer in the form at+bp=cat + bp = cat+bp=c, where a,b,ca, b, ca,b,c are integers.
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.
