The concentration of an enzyme, EEE micromoles per litre, in a bioreactor is monitored over a 6-hour cycle. The concentration at time TTT hours, where 0≤T≤60 \le T \le 60≤T≤6, is modeled by the equation:
E=T18(9+15T−2T2)+2 E = \frac{\sqrt{T}}{18}(9 + 15T - 2T^2) + 2 E=18T(9+15T−2T2)+2Given that EEE has a stationary value at T=αT = \alphaT=α:
Use calculus to show that α\alphaα satisfies the equation
10α2−45α−9=0 10\alpha^2 - 45\alpha - 9 = 0 10α2−45α−9=0Hence find the value of α\alphaα, giving your answer to 3 decimal places.
Use further calculus to prove that EEE is a maximum at this value of α\alphaα.
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.
