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If... f(0, 0,0) = 1, and Df (0,0,0) = 5, where 1 2 2 û = (¹/²). (55) √5 √5 then if we start at the origin and move .002 units in the direction of û, the value of the function should increase by about...

If... f(0, 0,0) = 1, and Df (0,0,0) = 5, where 1 2 2 û = (¹/²). (55) √5 √5 then if we start at the origin and move .002 units in the direction of û, the value of the function should increase by about...

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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If... ƒ(0, 0, 0) = 1, and Df₁ (0, 0, 0) = 5, where û - then if we start at the origin and move .002 units in the direction of û, the value of the function should increase by about... 2 2 √5' √5' √5 ✓/5). .002 units. .01 units 1 unit 2/√/5 units 5 units 10/√5 units
Transcribed Image Text:If... ƒ(0, 0, 0) = 1, and Df₁ (0, 0, 0) = 5, where û - then if we start at the origin and move .002 units in the direction of û, the value of the function should increase by about... 2 2 √5' √5' √5 ✓/5). .002 units. .01 units 1 unit 2/√/5 units 5 units 10/√5 units
Expert Solution
Step 1: Writing down the given information

Given that the directional derivative is D f subscript u with hat on top end subscript open parentheses 0 comma 0 comma 0 close parentheses equals 5.

The represents the rate of change of the function along the direction given by u with hat on top equals open parentheses fraction numerator 1 over denominator square root of 5 end fraction comma fraction numerator 2 over denominator square root of 5 end fraction comma fraction numerator 2 over denominator square root of 5 end fraction close parentheses.

At the origin, the function is f(0,0,0)=1.

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