4.2 Motivation for the calculus

Not all functions are straight lines

Their rate of change is not constant

These are the interesting relationships, e.g. diminishing returns

Often looking to find max/mins

Finding where curves cross the x-axis (zero's of a function)

Optimal ... everything (volatility estimators, portfolios, strategies

Optima usually correspond to derivatives equal to zero , which is why finding zeros is important

You need to get to know the shape/form of a function, it helps you make models and problem solve.

Questions to ask about functions:

Does it go uphill - positive derivative?

Downhill - negative derivative?

How steep is it - magnitude of the derivative (large or small)?

Does it have maxima/minima - derivative equals 0?