If (x+2y)dy/dx=2x-y, what is the value of d^2y/dx^2 at the point (3,0)?

Question

A. -10/3
B. 0
C. 2
D. 10/3
E. Undefined

Answer 1

using implicit derivatives,
(x+2y)y'=2x-y
(1+2y')y' + (x+2y)y" = 2-y'
Now plug in the numbers:
y'(3) = 2, so

(1+4)(2) + (3)y" = 2-2
10+3y" = 0
y" = -10/3