Respuesta :
The value at point ( 1, 1 ) is 8.
Explanation:
Given
3y³ = 2x⁹ + 1
y³ = 2/3x⁹ + 1/3
y = ∛2/3 x⁹ + 1/3
We need to first find dy/dx which is the first derivative and then d²y/dx² which is the second derivative
[tex]\frac{dy}{dx} = \frac{2x^8}{y^2}[/tex]
[tex]\frac{d^{2}y }{dx^2} = \frac{16x^7}{y^2} - \frac{8x^1^6}{y^5}[/tex]
Put the value of (1,1) : x = 1 and y = 1 in d²y/dx² equation
[tex]\frac{d^2y}{dx^2} = \frac{16 X 1^7}{1^2} - \frac{8 X 1^1^6}{1^5}[/tex]
[tex]\frac{d^2y}{dx^2} = 16 - 8\\\\\frac{d^2y}{dx^2} = 8[/tex]
Therefore, the value is 8.
