Mat 3.5:Implicit Differentiation

Question

x^3 + y^3 = 126. Find y''(x) at the point (5,1).

Answer 1

Hi Agent,

3x²+3y²y'=0

From algebra, y'=-x²/y²

Quotient Rule: y"=((-2x)(y²)-(-x²)(2yy'))/y⁴

At (5,1) or when x=5, y=1,

y"=((-10)(1)-(-25)(2y'))/1

=-10+50y'

y'(5,1)=-25 plug into first derivative.

So, =-10-1250=-1350

I hope this helps!