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+14where 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.
Use the remainder theorem to show that
16a+b=40 16a + b = 40 16a+b=40Given 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.
Find G′(s)G'(s)G′(s).
Hence find the exact coordinates of the stationary points of the curve with equation y=G(s)y = G(s)y=G(s).
Practise AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only), matched to the AQA A Level Maths (7357) 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.
