Consider the function f(x,y,z) = x⁴ + 2y³ + z². The directional derivative of the function at the point P(−1, 1, −1) along (î+ĵ), where î and ĵ are unit vectors in the x and y directions, respectively, rounded off to 2 decimal places, is _______

Question

Accepted Answer

The correct answer is 1.39 to 1.43. GATE 2024 official key: 1.39 to 1.43. ∇f=(4x³,6y²,2z); at (−1,1,−1): (−4,6,−2). Normalizing (î+ĵ) to (1,1,0)/√2, directional derivative = (−4+6+0)/√2 = 2/√2 = √2 ≈ 1.41.