Project ForgeEngineering Mathematics
Calculus
GATE 2019
Medium
The directional derivative of the function f(x,y)=x²+y² along a line directed from (0,0) to (1,1), evaluated at the point x=1, y=1 is
- A√2
- B2
- 2√2
- D4√2
Explanation
∇f=(2x,2y), which at (1,1) is (2,2). The unit vector from (0,0) to (1,1) is (1/√2,1/√2). Directional derivative = ∇f·û = 2(1/√2)+2(1/√2) = 4/√2 = 2√2.
Source: GATE ME 2019 Session 2 (Set 3) (2019)
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