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1.10 G: Differentiation

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Question 166

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

1.10 G: Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.10 G: Differentiation

375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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