1.3 Rates of Change

Main Points
Rates of change could also be calculated when changes in a certain value are not constant. and the formula used is: dy/dx = f(b) -f (a)/b -a. This formula thus calculate the average rates of change. When the average rate of change is the same at all intervals the functions is linear. A positive rate of change suggests an increase whilst a negative one suggests a decrease. The secant line is that with draws out the average rate of change of two points on a curve. This is also their slope. A concave up graph indicates that a function is increasing whilst a concave down graph has a decreasing function. In effect a line is constant.
The average rate of change of height per time is velocity this is different from speed, as speed is a magnitude that is either positive of zero and velocity is a vector. (ie. it can be negative as well.)

Challenges
Example 5 (a): between -1 and 2, I have no idea whether to say the function is increasing because as x increases and so does y, or to say it is decreasing because it is concave down.
And for the graph between x= 2 and 6, how would you describe wrt to (b) the first half is concave downa nd teh second is concave up...

Reflections
Again, being able to compute certain values using applied calculus and in this case rates of change one is able to predict future values for certain situations and thus act accordingly as they would be theorically prepared. But nothing that happens in theory ever happens exactly the same in real life.