Chapter 7 - Stationary Points Of Functions

Question 1

Definition of stationary point of a function of more than one variable

Answer 1

A point in the domain of the function such that the directional derivatives are zero

Question 2

F (x) has a local minimum at the point x0 if

Local minimum if

Answer 2

There exists a Dp (x0) such that
f (x) less than or equal to f (x0), for all x in Dp (x0)

F (x) bigger than or equal to f (x0)

Question 3

Local extremum

Answer 3

If a point P is either a local maximum or a local minimum

Question 4

Saddle point

Answer 4

A stationary point that isn’t a local maximum or minimum

Question 5

Taylor’s Theorem

Answer 5

F(a+h, b+k) = f(a,b) + fx(a,b)h + fy(a,b)k + 1/2! [fxx(a,b)h^2 + 2fxy(a,b)hk + fyy(a,b)k^2)

Question 6

P is a local minimum

Answer 6

If fxx >0 and fxxfyy - (fxy)^2 >0

Question 7

P is a local maximum

Answer 7

If fxxfyy-(fxy)^2 >0 and fxx <0