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If x^3-2x^2y^2+5x+y-5=0a n dy(1)=1,t h e...

If `x^3-2x^2y^2+5x+y-5=0a n dy(1)=1,t h e n` `y^(prime)(1)=4/3` (b) `y^(1)=-4/3` `y^(1)=-8(22)/(27)` (d) `y^(prime)(1)=2/3`

A

`y'(1)=4//3`

B

`y''(1)=-4//3`

C

`y''(1)=-8(22)/(27)`

D

`y'(1)=2//3`

Text Solution

Verified by Experts

`x^(3)-2x^(2)y^(2)+5x+y-5=0`
Differentiating w.r.t. x, we get
`3x^(2)-4xy^(2)-4x^(2)y(dy)/(dx)+5+(dy)/(dx)=0`
`"or "y'=(dy)/(dx)=(3x^(2)-4xy^(2)+5)/(4x^(2)y-1)`
`y'(1)=(3-4+5)/(4-3)=(4)/(1)`
Also, y''
`=((6x-4y^(2)-8xyy')(4x^(2)y-1)-(8xy+4x^(2)y')(3x^(2)-4xy^(2)+5))/((4x^(2)y-1)^(2))`
`"or "y''(1)=((6-4-8xx(4)/(3))(4-1)-(8+4xx(4)/(3))(3-4+5))/((4-1)^(2))`
`=-8(22)/(27)`
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