problem

Favourite

### Exponential Trend

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.

problem
###
Exponential Trend

Favourite

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.

problem
###
Quick Route

Favourite

What is the quickest route across a ploughed field when your speed
around the edge is greater?

problem
###
What's my equation?

Can you find the differential equations giving rise to these famous solutions?