1
Q
Global max
A
f(x*) > than all other values of f(x)
2
Q
Local max
A
f(x*) > than all other values of f(x) within an interval of x
3
Q
If f”(x)=0 what can we say about the type of stationary point?
A
Nothing. It could be a min, max or point of inflection
4
Q
What are the four steps for finding min/max in a banded interval
A
- Find critical points within interval
- Evaluate function at critical points
- Evaluate the function at x=a and x=b
- Choose the highest/lowest of f(x) from 2) and 3)
5
Q
When can we be sure that a function has a global max and min
A
If a continuous function exits in a closed and bounded interval then there is definitely a global max and min
6
Q
Sufficient first order condition text for global max
A
If f’(x)>=0 for x<=c and f’(x)<=0 for x>=c then x=c is a global max
7
Q
If f”(c)=0 and the f” changes sign at c and what can be said about c?
A
It is a point of inflection
