Project ForgeEngineering Mathematics
Calculus
GATE 2008
Medium
The directional derivative of f(x,y,z)=x²+2y²+z at P=(1,1,2) in the direction of the vector a=3î-4ĵ is
- A-4
- -2
- C-1
- D1
Explanation
∇f=(2x,4y,1)=(2,4,1) at P. Unit vector â=(3,-4,0)/5=(0.6,-0.8,0). Directional derivative=∇f·â=2(0.6)+4(-0.8)+1(0)=1.2-3.2=-2.
Source: GATE ME 2008 (2008)
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