A chemical engineer monitors the concentration, C C\,C mmol/L, of a reagent in a reaction vessel, which is modeled by the function
C(t)=4t+82t+1,t>−0.5 C(t) = \frac{4t + 8}{\sqrt{2t + 1}}, \quad t > -0.5 C(t)=2t+14t+8,t>−0.5where t t\,t is the time in minutes from the start of the reaction.
Find C′(t)C'(t)C′(t), giving your answer in simplest form.
Hence, determine the range of values for the concentration CCC.
Practise AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions 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), 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.
