Multiple choice

For a scalar function f(x, y, z) = x2 + 3y2 + 2z2, the gradient at the point P (1, 2, - 1) is

  1. $2i + 6 \bar{j} + 4 \bar{k}$
  2. $2i + 12 \bar{j} - 4 \bar{k}$
  3. $2i + 12 \bar{j} + 4 \bar{k}$
  4. $\sqrt{56}$
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B Correct answer
Explanation

The gradient of a scalar function f(x, y, z) is the vector (df/dx, df/dy, df/dz). Calculating these partial derivatives gives 2x, 6y, and 4z. Evaluating at (1, 2, -1) yields 2(1)i + 6(2)j + 4(-1)k, which is 2i + 12j - 4k.

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