A-level maths help :(

Hello, So I got all other parts correct except for part c). Now I thought that the maximum rate of growth would be when dN/dt is equal to 0 and then you could just set the numerator equal to 0 but it's apparently when the second derivative is 0 and I do not know why.

- Is it because dy/dx tells us if there is a turning point and there second derivative tells us the nature of that stationary point

(edited 11 months ago)

Screenshot 2023-05-18 192534.png257.4KB

Reply 1

mqb2766

dN/dt is the rate of growth, so that will be stationary (maximum) when its derivative is zero, so you need
d^2N/dt^2=0

Its a bit like saying dx/dt is velocity (where velocity is rate of change of displacement x) and velocity is maximum/stationary when acceleration (rate of change of velocity), d^2x/dt^2, is zero.