Edexcel | A-Level June 2018 Pure Maths Paper 2 Question 14(c) | ExamSolutions 

For anyone that is interested you have to read the question Very carefully, the question mentions that "the rate of growth" (dn/dt) is a maximum not "N". Quite a nasty addition that catches a-lot of people. You can still use the same principles though, this method also works by setting the second derivative equal to zero and solving as you normally would (I'd argue that's the easiest way to complete this question); a good example of why second derivates, third derivatives and so on have their uses. In other terms, if you know that the gradient function "dn/dt) has a maximum then you know the gradient function of the gradient function (in other terms the second derivative) has stationary points equal to zero and then, you solve as usual. Hope this helps