Verify that the curve f(x,y) =5x² - 6xy + 5y² = 2 passes through the point P=((1) /√2,(1) /√2) and calculate the gradient vector of the curve at P. What is the equation of the tangent line?
a) Equation: y = x, Gradient vector: [2, -2]
b) Equation: y = -x, Gradient vector: [2, 2]
c) Equation: y = x, Gradient vector: [2/√2, -2/√2]
d) Equation: y = -x, Gradient vector: [2/√2, 2/√2]