Let f : R²→ R be defined by: 1 f (x) = (2x1 + x2 + 1)²" (a) Find the directional derivative at xº = (0,0) in direction v = (1, 1) . %3D (b) Find the best quadratic approximation of the function at xº = (0,0). %3D
Let f : R²→ R be defined by: 1 f (x) = (2x1 + x2 + 1)²" (a) Find the directional derivative at xº = (0,0) in direction v = (1, 1) . %3D (b) Find the best quadratic approximation of the function at xº = (0,0). %3D
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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![Let \( f : \mathbb{R}^2 \to \mathbb{R} \) be defined by:
\[
f(x) = \frac{1}{(2x_1 + x_2 + 1)^2}.
\]
(a) Find the directional derivative at \( x^0 = (0, 0) \) in direction \( v = (1, 1) \).
(b) Find the best quadratic approximation of the function at \( x^0 = (0, 0) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7f4e788-ef76-42cd-ba71-0d980b205d9f%2Ff68efd94-abab-4020-871f-5013186f1c96%2Fd1y2uvi_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( f : \mathbb{R}^2 \to \mathbb{R} \) be defined by:
\[
f(x) = \frac{1}{(2x_1 + x_2 + 1)^2}.
\]
(a) Find the directional derivative at \( x^0 = (0, 0) \) in direction \( v = (1, 1) \).
(b) Find the best quadratic approximation of the function at \( x^0 = (0, 0) \).
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