Real Analysis Real Analysis Math Forum

 May 6th, 2012, 09:08 AM #1 Senior Member   Joined: Sep 2008 Posts: 105 Thanks: 0 Gradient Consider the function f defined by 1) f(x,y) = 0 unless x>0 and $x^2 < y < 3x^2$ 2) for each x > 0$f(x, 2x^2)= x$ 3) $0 \leq f(x,y) \leq x$ for all (x,y) with x>0 Modify this to get a function g with $g_1 (0,0)=g_2 (0,0) = 1$ yet there is no direction of maximal change. I know f has no direction of maximal change because$f_1 (0,0)$and$f_2 (0,0$) are both 0, and so the gradient is zero and the angle between the gradient and any direction vector is undefined. How can this happen when the gradient is 1?

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post jiasyuen Calculus 5 January 9th, 2014 10:55 AM coachcft Calculus 2 December 15th, 2012 12:25 PM truthseeker Linear Algebra 12 October 2nd, 2012 07:07 AM dthomas86 Calculus 5 December 30th, 2011 03:21 AM dthomas86 Algebra 3 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top