Question 25 – 9.9 Using Second Derivatives - Questions

A scientist is modeling the depletion of a reactant in a chemical solution. The concentration $C (t)$ over time $t$ is known to be a convex (concave up) function for all $t > 0$ . Identify which of the following qualitative descriptions of the concentration-time graph correctly represents $C (t)$ .

Graph A: The concentration decreases over time, but the rate of decrease slows down, meaning the gradient $C^{'} (t)$ is strictly increasing towards zero.

Graph B: The concentration increases over time, but each subsequent increase is smaller than the last, meaning the gradient $C^{'} (t)$ is strictly decreasing.

Graph C: The concentration increases and then decreases, reaching a clear peak at a local maximum.

Graph D: The concentration decreases over time, and the rate of decrease accelerates, meaning the gradient $C^{'} (t)$ becomes more negative as $t$ increases.

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.

Graph A: The concentration decreases over time, but the rate of decrease slows down, meaning the gradient $C^{'} (t)$ is strictly increasing towards zero.

Graph B: The concentration increases over time, but each subsequent increase is smaller than the last, meaning the gradient $C^{'} (t)$ is strictly decreasing.

Graph C: The concentration increases and then decreases, reaching a clear peak at a local maximum.

Graph D: The concentration decreases over time, and the rate of decrease accelerates, meaning the gradient $C^{'} (t)$ becomes more negative as $t$ increases.