Advanced Calculus: The Mean Value Theorem and Directional Derivatives
Not what you're looking for? Search our solutions OR ask your own Custom question.
This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!
Please see the attached file for the fully formatted problems.
Let F: R^n --> R be continuously differentiable. Show that at each point x E R^n there is a direction hx so that the directional derivative is 0, i.e., df/dhx (x) = 0. Is hx unique? Give a method for determining hx.© BrainMass Inc. brainmass.com May 24, 2023, 1:22 pm ad1c9bdddf
Please see the attached file for the complete solution.
Thanks for using BrainMass.
Proof: Since is continuously differentiable, then exists. is defined as . Now for any ...
A proof involving directional derivatives is provided. The solution is detailed.