Given f(x,y)=x(y^2)+y(e^2). What is the directional derivative at (x,y) at (0,1)
Favorites|Homepage
Subscriptions | sitemap
HOME > > Given f(x,y)=x(y^2)+y(e^2). What is the directional derivative at (x,y) at (0,1)

Given f(x,y)=x(y^2)+y(e^2). What is the directional derivative at (x,y) at (0,1)

[From: ] [author: ] [Date: 11-12-08] [Hit: ]
1)||.So, D_u f(0,= ∇f(0,= ∇f(0, 1) · [∇f(0,......
Find the directional derivative at (x,y) at (0,1) along the direction of the most rapid increase of f.

Thanks for helping!!

-
This is in the direction of ∇f(0, 1) = {at (0, 1)} = <1, e^2>.
==> u = ∇f(0, 1)/||∇f(0, 1)||.

So, D_u f(0, 1)
= ∇f(0, 1) · u
= ∇f(0, 1) · [∇f(0, 1)/||∇f(0, 1)||]
= ||∇f(0, 1)||
= √(1 + e^4).

I hope this helps!
1
keywords: derivative,Given,the,at,What,directional,is,Given f(x,y)=x(y^2)+y(e^2). What is the directional derivative at (x,y) at (0,1)
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .