To find the second derivative of the function y=x-6/x at the point x0=2, we need to first find the first derivative and then differentiate it again.
First find the first derivative:y = x - 6/xy' = 1 + 6/x^2
Now differentiate y' with respect to x to find the second derivative:y" = d/dx (1 + 6/x^2)y" = 0 - 12/x^3y" = -12/x^3
Now, substitute x=2 into the equation to find the value of the second derivative at x0=2:y" = -12/(2)^3y" = -12/(8)y" = -1.5
Therefore, the second derivative of the function y=x-6/x at the point x0=2 is y" = -1.5.
To find the second derivative of the function y=x-6/x at the point x0=2, we need to first find the first derivative and then differentiate it again.
First find the first derivative:
y = x - 6/x
y' = 1 + 6/x^2
Now differentiate y' with respect to x to find the second derivative:
y" = d/dx (1 + 6/x^2)
y" = 0 - 12/x^3
y" = -12/x^3
Now, substitute x=2 into the equation to find the value of the second derivative at x0=2:
y" = -12/(2)^3
y" = -12/(8)
y" = -1.5
Therefore, the second derivative of the function y=x-6/x at the point x0=2 is y" = -1.5.