1.3 & 2.1 Rates of change and the derivative

Main points:
• Average rate of change of y between t=a and t=b: delta(y)/delta(t)=[f(b)-f(a)]/(b-a)
• The units of average rate of change of a function are units of y per unit of t
• Increasing function: the values of f(x) increase as x increases
• Decreasing function: the values of f(x) decrease as x increases
• Concavity
○ Concave up=bends upwards as we move left to right
○ Concave down=bends downwards as we move left to right
• Average velocity=change in distance/change in time
• Instantaneous velocity of an object at time t is defined to be the limit of the average velocity of the object over shorter and shorter time intervals containing t
• Instantaneous rate of change of f at a (also known as rate of change of f at a) is defined to be the limit of the average rates of change of f over shorter and shorter intervals around a
• Derivative of f at a, f'(a), is defined to be the instantaneous rate of change of f at the point a

Challenges:
It is a long time since I have last done physics so problems with velocity are going to be good practice for me. Other ways derivatives are something what I did study in the past but don’t really remember anymore, so I am going to need some practice with them too. I am also finding myself in need to recap the basic precalculus things, in order to work with the current problems. So I need to set more time for revision of things I have learnt in the past.

Reflection:

The derivatives totally took my attention, as they are needed in so many different sciences. I also didn’t understand them too well in the past so I am looking forward to become more familiar with them. Most of the problems were related to hard sciences and I was hoping to see more problems from economics (especially in the derivatives section). I hope there are going to be some economics related problems in tomorrow's class.