If...ƒ(0, 0, 0) = 1,andDf₁ (0, 0, 0) = 5,whereû-then if we start at the origin and move .002 units in the direction of û, the value of the functionshould increase by about...22√5' √5' √5✓/5)..002 units..01 units1 unit2/√/5 units5 units10/√5 units

Given that the directional derivative is The represents the rate of change of the function along the…

Answered: If... f(0, 0,0) = 1, and Df (0,0,0) =…

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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Related questions

Question

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 $f (0, 0, 0) = 1.$