Partial Diff

Question 1

Total derivative

Answer 1

dF = (𝜕F/𝜕x) dx + (𝜕F/𝜕y) dy

Question 2

Finding stationary point

Answer 2

𝜕F/𝜕x = 𝜕F/𝜕y = 0

Question 3

Classifying Stationary points Formula

Answer 3

Δ = (Fxy(a,b))^2-Fxx(a,b)Fyy(a,b) where a and b are the coordinates of the stationary point

Question 4

Classifying stationary points meaning

Answer 4

Δ>0 Saddle point
Δ<0 and Fxx(a,b)<0 Max
Δ<0 and Fxx(a,b)>0 Min

Question 5

dΦ/dr

Answer 5

(δΦ/δx)(δx/δr) + (δΦ/δy)(δy/δr)

Question 6

dΦ/dθ

Answer 6

(δΦ/δx)(δx/δθ) + (δΦ/δy)(δy/δθ)