Question

Compute d2y/dx2 at the point (4, 3).
x^2-y^2 = 7

Answer 1

dx^2/dx - dy^2/dx = d7/dx = 0. So,
2x-(dy^2/dy)(dy/dx)=0,
2x-2y(dy/dx)=0,
x-y(dy/dx)=0,
x=y(dy/dx),
x/y=dy/dx, dy/dx=x/y,
d^2y/dx^2=d(x/y)/dx=[(dx/dx)y-x(dy/dx)]/y^2,
d^2y/dx^2=[1y-x(dy/dx)]/y^2, substituing dy/dx by x/y
d^2y/dx^2=[1y-x^2y]/y^2, in the point(4,3), x=4 and y=3. So,
d^2y/dx^2=[3-(4^2)3]/3^2,
Then, d^2y/dx^2=[3-48]/9=-5

Answer 2

there are answer choices

Answer 3

which one is it? ill post it now

Answer 4

a) 7/27
b)- 7/27
c) 14/ 27
d) - 14/27
e) - 7/9

Answer 5

oh sorry, in the 3rd line from down to up the coorect is
d^2y/dx^2=[1y-(x^2)/y]/y^2, so substituing
d^2y/dx^2=[3-(4^2)/3]/(3^2). Then,
d^2y/dx^2=-7/27, letterb

Answer 6

thank you....i was kinda confused y u got five wen its not in any of the answer choices

Answer 7

no problem