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Differentiation

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Question 436

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]
Markscheme

Differentiation Questions

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

717 exam-style questions on Edexcel A Level Maths Differentiation, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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