2. Centered-difference formula for the second derivative with two independent variables r and y a?u (x, y) = и(х+h.у ) — 2и(х,у)+и(х-h-у) и (§ , y ) 12 ax4 h? a²u (x , y) = h² a+u - (1 , η ) 12 əy4 и(x.y+h) — 2u(х .у) +и(х.у-h) where { E (x – h,x + h) and 7 E (y – h, y + h).

Find y''. X y = 4 cot (76) 10 O A. OB. 2 25 O C. - 8 csc O D. CSC 2 5 2 CSC 2 X 10 X 10 X 10 cot X 10 X X 2 8 csc ² [+] cot (16) 圖 10 10

Find the directions in which f increases and decreases most rapidly at point P. Then find the derivatives of f in these directions. f(x, y) = 3x? + 2xy+ 4y², P = (7,8) Direction of fastest increase is Direction of fastest decrease is Derivative in the direction of fastest increase is Derivative in the direction of fastest decrease is f(х, у) — х? у + е2хy sin(y), Р 3 (-3, 0) Direction of fastest increase is Direction of fastest decrease is Derivative in the direction of fastest increase is Derivative in the direction of fastest decrease is