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1.3 Functions

1.3 Functions

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Question 88

A chemical engineer models the temperature gradient G(s)G(s)G(s) (in °C/cm) along a cooling fin, where s s\,s is the distance from the heat source in cm, as:

G(s)=as3−9s2+bs+14 G(s) = as^3 - 9s^2 + bs + 14 G(s)=as3−9s2+bs+14

where a a\,a and b b\,b are constants.

When G(s)G(s)G(s) is divided by (s−4)(s - 4)(s−4), the remainder is 30.

a.

Use the remainder theorem to show that

16a+b=40 16a + b = 40 16a+b=40
[3]
b.

Given also that (s−1)(s - 1)(s−1) is a factor of G(s)G(s)G(s),

find the value of a a\,a and the value of bbb.

[3]
c.

Find G′(s)G'(s)G′(s).

[2]
d.

Hence find the exact coordinates of the stationary points of the curve with equation y=G(s)y = G(s)y=G(s).

[4]
Markscheme

1.3 Functions Questions

  1. A Level
  2. /Maths
  3. /1.3 Functions

181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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