I have the function $$ f(x,y) = 0.5(0.7x-0.3y)^2 + \frac{1}{3}(0.7y-0.3x)^2$$
Constraint : $$g(x,y) = 2+0.6x-y$$
Parametrization of $$g(x,y) => h(x) = (h_1(x),h_2(x))^T = (x , 2+0.6x)^T$$
The solution for the gradient is as follows:
$$\nabla (x,h_2(x)) = (0.34x-0.7, -0.1x + 0.833...)^T$$
Tangent vector is given by: $$ t = (h_1(x)',h_2(x)')^T = (1,0.6)^T$$
At $$ x = x^*, y = h_2(x^*) = y^* $$
Scalar product should be zero:
$$ t \cdot \nabla (x^*,y^*) = 0.28x^* -0.2 = 0$$
However my calculations give me $$ -0.26x^* -0.2 = 0$$
Is the handout solution wrong or where is my mistake?