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ก้าวต่อก้าว

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

   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. \frac{\partial f}{\partial z} = 2 z

   Treat every variable except z as a constant.

5. \nabla f = \left[\begin{matrix}2 x\\2 y\\2 z\end{matrix}\right]

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

6. (0, 0, 0)

   Critical points: where every partial derivative is zero.

เปิดเผยคำตอบ

\nabla f = \left[\begin{matrix}2 x\\2 y\\2 z\end{matrix}\right]