(b) Find the following directional derivative f'(x; v) for the following functions at the given x and v. (The functions refer to part (a)) - (-1); v = (3) (-₁); v anything ONLY PART B - PLESAE (i) fi(); x = (iii) f3(-); x = (ii) f₂(); x = (iv) f₁(); x = (³); v = (₂2) (3); v = (-2¹)
(b) Find the following directional derivative f'(x; v) for the following functions at the given x and v. (The functions refer to part (a)) - (-1); v = (3) (-₁); v anything ONLY PART B - PLESAE (i) fi(); x = (iii) f3(-); x = (ii) f₂(); x = (iv) f₁(); x = (³); v = (₂2) (3); v = (-2¹)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Practice II.1. Consider the case n = 2.
(a) Find the gradients of the following functions from R² to R:
:= x² + x²-2
(ii) ƒ₂ (21) := 4x² +
(i) fi
(iii) f3
21
I2
I1
I₂
:= 9(x₁ − 1)² + (2+¹)²-2 (iv) f₁
(i) fi(.); x =
• (-¹1); v = (3)
=(-¹)
ONLY PART B - PLESAE
(b) Find the following directional derivative f'(x; v) for the following functions at
the given x and v. (The functions refer to part (a))
(iii) f3(-); x =
I1
In
v anything
1:= = √(x₁ + 1)² + (x₂ - 2)²
=4x²+2-1
(ii) f2(.); x =
(iv) f₁(); x =
(3);
3
(2)
- (2¹)
V =
V =
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To Find : Directional Derivative of
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