9.9 Using Second Derivatives

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The pressure $P$ (in pascals) within a reaction vessel varies with time $t$ (in seconds) according to the function

$P(t) = t^3 - ct^2 + 3t - 8$

where $c\,$ is a positive constant.

Find, in simplest form, (i) $P^{'} (t)$ (ii) $P^{''} (t)$

[2]

The curve with equation $y = P^{'} (t)$ intersects the curve with equation $y = P^{''} (t)$ at the points $A\,$ and $B$ .

Given that the $t$ -coordinate of $A\,$ is 5,

find the value of $c$ .

[2]

Hence find the coordinates of $B$ .

[3]

9.9 Using Second Derivatives Questions

Practise Edexcel A Level Maths 9.9 Using Second Derivatives with exam-style questions for A Level Maths. 57 questions, 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.