Foraging Many animals forage on resources that are distributed in discrete patches. For example, bumblebees visit many flowers, foraging on nectar from each. The amount of nectar Nstd consumed from any flower increases with the amount of time spent at that flower, but with diminishing returns, as illustrated.

(a) What does this mean about the first and second derivatives of N?

(b) What is the average rate at which nectar is consumed over the first 10 seconds?

(c) The Mean Value Theorem tells us that there exists a time at which the instantaneous rate of nectar consumption is equal to the average found in part (b). Illustrate this idea graphically and estimate the time at which this occurs.

N^(mg) 0.1- 0 5. 10 t (seconds)