4.No justification is necessary for any part below. Let f : R2 →R be C2 and fix p = (2,37) € R?.Suppose f(p) = 5, Vf(p) = (-1,2), and Hf (p) =6(4a) Write the Jacobian of f at p and the value of fyy(p).Df (p) =fyy(p) =(4b) Compute D,f (p) where v = (1,3).D,f (p) =(4c) Give an explicit formula for the differential of f at p.(4d) For which unit vector u eR? is the quantity Df (p) minimized?u =(4e) Let S = {(x, y) ER? : f(x, y) = 5}. Write down the tangent line of S at p using set builder notation.p+ T,S =(4f) Approximate f (2.5,36) with a second order approximation. Recall p = (2,37).f (2.5, 36)

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Description: 4.No justification is necessary for any part below. Let f : R2 →R be C2 and fix p = (2,37) € R?.Suppose f(p) = 5, Vf(p) = (-1,2), and Hf (p) =6(4a) Write the Jacobian of f at p and the value of fyy(p).Df (p) =fyy(p) =(4b) Compute D,f (p) where v = (

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No justification is necessary for any part below. Let f : R² → R be C2 and fix p = (2,37) E R?. [2 0 4. Suppose f(p) = 5, Vf(p) =(-1,2), and Hƒ (p) =6 : (4a) Write the Jacobian of f at p and the value of fyy (p). Df (p) = fyy(p) = (4b) Compute D,f (p) where v = (1,3). %3! D,f (p) = (4c) Give an explicit formula for the differential of f at p.

No justification is necessary for any part below. Let f : R² → R be C2 and fix p = (2,37) E R?. [2 0 4. Suppose f(p) = 5, Vf(p) =(-1,2), and Hƒ (p) =6 : (4a) Write the Jacobian of f at p and the value of fyy (p). Df (p) = fyy(p) = (4b) Compute D,f (p) where v = (1,3). %3! D,f (p) = (4c) Give an explicit formula for the differential of f at p.

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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Question

4.
No justification is necessary for any part below. Let f : R2 →R be C2 and fix p = (2,37) € R?.
Suppose f(p) = 5, Vf(p) = (-1,2), and Hf (p) =6
(4a) Write the Jacobian of f at p and the value of fyy(p).
Df (p) =
fyy(p) =
(4b) Compute D,f (p) where v = (1,3).
D,f (p) =
(4c) Give an explicit formula for the differential of f at p.
(4d) For which unit vector u eR? is the quantity Df (p) minimized?
u =
(4e) Let S = {(x, y) ER? : f(x, y) = 5}. Write down the tangent line of S at p using set builder notation.
p+ T,S =
(4f) Approximate f (2.5,36) with a second order approximation. Recall p = (2,37).
f (2.5, 36)

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