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Differentiation

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Question 183

The pressure PPP (in pascals) within a reaction vessel varies with time ttt (in seconds) according to the function

P(t)=t3−ct2+3t−8 P(t) = t^3 - ct^2 + 3t - 8 P(t)=t3−ct2+3t−8

where c c\,c is a positive constant.

a.

Find, in simplest form, (i) P′(t)P'(t)P′(t) (ii) P′′(t)P''(t)P′′(t)

[2]
b.

The curve with equation y=P′(t)y = P'(t)y=P′(t) intersects the curve with equation y=P′′(t)y = P''(t)y=P′′(t) at the points A A\,A and BBB.

Given that the ttt-coordinate of A A\,A is 5,

find the value of ccc.

[2]
c.

Hence find the coordinates of BBB.

[3]

Differentiation Questions

  1. A Level
  2. /Maths
  3. /Differentiation

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.

Question bank