2. Optimisation

Question 1

Global max

Answer 1

f(x*) > than all other values of f(x)

Question 2

Local max

Answer 2

f(x*) > than all other values of f(x) within an interval of x

Question 3

If f”(x)=0 what can we say about the type of stationary point?

Answer 3

Nothing. It could be a min, max or point of inflection

Question 4

What are the four steps for finding min/max in a banded interval

Answer 4

1. Find critical points within interval
2. Evaluate function at critical points
3. Evaluate the function at x=a and x=b
4. Choose the highest/lowest of f(x) from 2) and 3)

Question 5

When can we be sure that a function has a global max and min

Answer 5

If a continuous function exits in a closed and bounded interval then there is definitely a global max and min

Question 6

Sufficient first order condition text for global max

Answer 6

If f’(x)>=0 for x<=c and f’(x)<=0 for x>=c then x=c is a global max

Question 7

If f”(c)=0 and the f” changes sign at c and what can be said about c?

Answer 7

It is a point of inflection