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.
115 exam-style questions on CCEA A Level Maths 1.6 Differentiation, covering 1.6.1 Differentiation, 1.6.2 Differentiation, 1.6.3 Differentiation, 1.6.4 Differentiation, 1.6.5 Differentiation, 1.6.6 Differentiation, and 1.6.7 Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.