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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

1. -4
2. -2
3. -1
4. 1

Correct answer: -2

Solution

The directional derivative is calculated by taking the dot product of the gradient of the function at the given point and the unit vector in the direction of the specified vector. At point P, the gradient of the function is evaluated, and when the unit vector of the direction is used, the resulting value is -2.

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