9.9 Using Second Derivatives

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The concentration, $C$ , of a reactant in a non-isothermal chemical process is modeled by the function $\phi(t)$ , where $t$ is the time in seconds. It is known that the graph of $C$ against $t$ has a point of inflection at $t = 12$ . Given that $ϕ′(12)=a\phi'(12) = a$ and $ϕ′′(12)=b\phi''(12) = b$ , where $a$ and $b$ are constants,

identify which of the following statements must be true:

$ϕ′(12)=0\phi'(12) = 0$ $ϕ′′(12)=0\phi''(12) = 0$ $ϕ′(12)≠0\phi'(12) \neq 0$ $ϕ′′(12)>0\phi''(12) > 0$

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9.9 Using Second Derivatives Questions

Practise Edexcel A Level Maths 9.9 Using Second Derivatives with exam-style questions for A Level Maths. 57 questions, 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.