ريا طي مسائل کو حل کريں

قدم ب قدم

1. f(x, y) = x^{3} - 3 x + y^{2}

   The gradient is the vector of partial derivatives — differentiate with respect to each variable, holding the others constant.

2. \frac{\partial f}{\partial x} = 3 x^{2} - 3

   Treat every variable except x as a constant.

3. \frac{\partial f}{\partial y} = 2 y

   Treat every variable except y as a constant.

4. \nabla f = \left[\begin{matrix}3 x^{2} - 3\\2 y\end{matrix}\right]

   Assemble the gradient vector. It points in the direction of steepest ascent.

5. (-1, 0),\ (1, 0)

   Critical points: where every partial derivative is zero.