The relationship between the pressure $p$ and temperature $t$ of a specific gas model is described by the equation

p^3t + 2pt^3 = 12

Prove that the curve representing this relationship does not intersect the coordinate axes in the $p$ - $t$ plane.

Show that

\frac{dt}{dp} = -\frac{3p^2t + 2t^3}{p^3 + 6pt^2}

Prove that the model has no stationary points.

In the case when $p > 0$ , find the equation of the tangent line to the curve at the point where $t = 1$ . Give your answer in the form $a t + b p = c$ , where $a, b, c$ are integers.

The relationship between the pressure $p$ and temperature $t$ of a specific gas model is described by the equation

p^3t + 2pt^3 = 12

Prove that the curve representing this relationship does not intersect the coordinate axes in the $p$ - $t$ plane.

Show that

\frac{dt}{dp} = -\frac{3p^2t + 2t^3}{p^3 + 6pt^2}

Prove that the model has no stationary points.

In the case when $p > 0$ , find the equation of the tangent line to the curve at the point where $t = 1$ . Give your answer in the form $a t + b p = c$ , where $a, b, c$ are integers.

1 Pure Mathematics

Question 87

Markscheme

1 Pure Mathematics

Question 87

Markscheme

1 Pure Mathematics

Question 87

1 Pure Mathematics Questions

1 Pure Mathematics

Question 87

1 Pure Mathematics Questions