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9.9 Using Second Derivatives

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Question 23

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]

Markscheme

9.9 Using Second Derivatives Questions

A Level
Maths
9.9 Using Second Derivatives

57 exam-style questions on Edexcel A Level Maths 9.9 Using Second Derivatives. Each one has a worked solution and a mark scheme showing where the marks go.

9.9 Using Second Derivatives

Question bank

9.9 Using Second Derivatives

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Question 23

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]

Markscheme

9.9 Using Second Derivatives Questions

A Level
Maths
9.9 Using Second Derivatives

57 exam-style questions on Edexcel A Level Maths 9.9 Using Second Derivatives. Each one has a worked solution and a mark scheme showing where the marks go.