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The directional derivative of the scalar function f(x, y, z) = x2 + 2y2 + z at the point P = (1, 1, 2) in the direction of the vector a = 3î - 4ĵ is
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- –4
- –2
- –1
- 1
Correct Option: B
The directional derivative of a function Φ along a vector A is given by,
| (grad Φ). | | A | |
Hence directional derivative is
| (grad (x2 + 2y2 + z)). | √32 + 42 |
| (2xî + 4yĵ + k̂), | 5 |
| = | 5 |
Hence (1, 1, 2), directional derivative
| = | = - 2 | 5 |
