Question

If 5x^2 + y^4 = −9 then evaluate d^2y/dx^2 when x = 2 and y = 1. Round your answer to two decimal places.

Answer 1

The first derivative is found from
.. 10x +4y^3*dy/dx = 0
.. dy/dx = -5x/(2y^3)

Then
.. d^2y/dx^2 = d(dy/dx)/dx = (-5/2)(y^-3 -3xy^-4*dy/dx)

Evaluated at x=2, y=1
.. dy/dx = -5(2)/(2*1^3) = -5
.. d^2y/dx^2 = (-5/2)*(1^-3 -3*2*1^-4*(-5))
.. = (-5/2)(1 +30)
.. = -155/2 = -77.50

d^2y/dx^2 = -77.50 at the specified point.