### Real(ly) Numbers

If x, y and z are real numbers such that: x + y + z = 5 and xy + yz + zx = 3. What is the largest value that any of the numbers can have?

### How Many Solutions?

Find all the solutions to the this equation.

### After Thought

Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?

# Exponential Trend

##### Stage: 5 Challenge Level:

In order to differentiate this function and to find the turning points express it in the form $x^{1/x} = e^{1/x \log x}.$