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6. Given f(x, y) = 2x³y=x²y³, a) find the directional derivative of f(x, y) at (1, 1) in the direction of (5, 12) b) find the maximum value of directional derivative at (1,1) and the direction in which this occurs. c) Find the equation of the tangent line in parametric form at the point (1.1, f(1,1)) in the direction of the vector v=(5, 12)

6. Given f(x, y) = 2x³y=x²y³, a) find the directional derivative of f(x, y) at (1, 1) in the direction of (5, 12) b) find the maximum value of directional derivative at (1,1) and the direction in which this occurs. c) Find the equation of the tangent line in parametric form at the point (1.1, f(1,1)) in the direction of the vector v=(5, 12)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6. Given \( f(x, y) = 2x^3y - x^2y^3 \), a) Find the directional derivative of \( f(x, y) \) at \( (1, 1) \) in the direction of \( \langle 5, 12 \rangle \). b) Find the maximum value of the directional derivative at \( (1, 1) \) and the direction in which this occurs. c) Find the equation of the tangent line in parametric form at the point \( (1, 1, f(1, 1)) \) in the direction of the vector \( \vec{v} = \langle 5, 12 \rangle \).
Transcribed Image Text:6. Given \( f(x, y) = 2x^3y - x^2y^3 \), a) Find the directional derivative of \( f(x, y) \) at \( (1, 1) \) in the direction of \( \langle 5, 12 \rangle \). b) Find the maximum value of the directional derivative at \( (1, 1) \) and the direction in which this occurs. c) Find the equation of the tangent line in parametric form at the point \( (1, 1, f(1, 1)) \) in the direction of the vector \( \vec{v} = \langle 5, 12 \rangle \).
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