Help me fast....with proper explanation Consider the directional derivative of the general function z= f(x,y).a)Where is it ai)maximum?ii)minimum?b)Where is it0?ii)half its maximum valuShow that every normal line to the sp

Answered: Consider the directional derivative of…

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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Help me fast....with proper explanation

Consider the directional derivative of the general function z= f(x,y).
a)
Where is it a
i)
maximum?
ii)
minimum?
b)
Where is it
0?
ii)
half its maximum valu
Show that every normal line to the sp

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$T h e d i r e c t i o n a l d e r i v a t i v e o f f u n c t i o n φ = z - f (x, y) a t (a, b, c) i n t h e d i r e c t i o n o f u i s D_{u} φ = \nabla φ (a, b, c) . \frac{u}{|u|} m o d u l u s o f d i r e c t i o n a l d e r i v a t i v e = |\nabla φ (a, b, c)| \cos θ a . 1 . w h e n θ = 0^{0} \Rightarrow \cos θ = 1 t h e d i r e c t i o n a l d e r i v a t i v e i s m a x i m u m a n d t h e v a l u e i s |\nabla φ (a, b, c)| 2 . w h e n θ = 180^{0} \Rightarrow \cos θ = - 1 t h e d i r e c t i o n a l d e r i v a t i v e i s m i n i m u m a n d v a u e i s - |\nabla φ (a, b, c)|$

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