Week 3 Partial Differentiation

Question 1

when do you use partial differentiation

Answer 1

when you need to differentiate multiple variables

Question 2

what happens if our variables are themselves made up of variables
e.g. f(x, y) –> x(s,t) and y(s,t)

Answer 2

the partial differentiation of the function f wrt to one of the variables (s or t) is equal to
∂f/∂s = (∂f/∂x)(∂x/∂s) + (∂f/∂y)(∂y/∂s)

Question 3

what does partial differentiation allow us to do

Answer 3

we can change variables so can change between cartesian and polar coordinates

Question 4

what is the main characteristic of a stationary point

Answer 4

the first derivative at that point will be 0

Question 5

what are the 3 types of stationary point

Answer 5

maxima
minima
saddle/inflection

Question 6

what is the procedure for finding the type of a stationary point

Answer 6

1 set the first derivative to 0
2 do the second order partial derivatives for fxx fxy and fyy
3 find Δ where Δ = f^2xy-fxxfyy
4 if Δ > 0 it is a saddle 
   if Δ < 0 & fxx < 0 its a maxima
   if Δ < 0 & fxx > 0 its a minima