The concentration, CCC, of a reactant in a non-isothermal chemical process is modeled by the function C=ϕ(t)C = \phi(t)C=ϕ(t), where ttt is the time in seconds. It is known that the graph of CCC against ttt has a point of inflection at t=12t = 12t=12. Given that ϕ′(12)=a\phi'(12) = aϕ′(12)=a and ϕ′′(12)=b\phi''(12) = bϕ′′(12)=b, where aaa and bbb are constants,
identify which of the following statements must be true:
ϕ′(12)=0 \phi'(12) = 0 ϕ′(12)=0 ϕ′′(12)=0 \phi''(12) = 0 ϕ′′(12)=0 ϕ′(12)≠0 \phi'(12) \neq 0 ϕ′(12)=0 ϕ′′(12)>0 \phi''(12) > 0 ϕ′′(12)>0Practise 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.
