Question

The force in an electrostatic field given by f(x, y, z) has the direction of the gradient. Find ∇f and its value at P.

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Given a differentiable function f:R2Rf:\mathbb{R}^2\to\mathbb{R}, it's gradient f\nabla f is a function from R2\mathbb{R}^2 to R2\mathbb{R}^2. At a point (x,y)(x,y), the direction of f(x,y)\nabla f(x,y) points to the direction of the greatest growth of ff, and it's magnitude tells us the speed of this growth.

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