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 Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change, matched to the Edexcel A Level Maths (9MA0) 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.
