Quotient rule

There are 3 NRICH Mathematical resources connected to Quotient rule
Placeholder: several colourful numbers
problem

Bird-Brained

Age
16 to 18
Challenge level
filled star empty star empty star
How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.
What's my equation?
problem

What's my equation?

Age
16 to 18
Challenge level
filled star filled star filled star
Can you find the differential equations giving rise to these famous solutions?
Exponential Trend
problem

Exponential Trend

Age
16 to 18
Challenge level
filled star empty star empty star
Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.