Explore BrainMass

Explore BrainMass

    Directional Derivative and Tangent Vector

    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!

    Give a simple proof or counterexample to disprove:

    If tangent vector p E Rn is such that the directional derivative of f by k vanished for every function f then k =0.

    If function f on Rn is such that the directional derivative of f by every tangent vector at every point vanishes, then f is constant.

    The directional derivative of the product of two functions product of their directional derivatives.

    © BrainMass Inc. brainmass.com December 24, 2021, 5:09 pm ad1c9bdddf


    Solution Preview

    Please see the attached file for the complete solution.
    Thanks for using BrainMass.

    a) It is true.
    Proof. Without loss of generality, we assume that n=2. To the contrary, suppose that . Then for a function , its directional derivative with respect to at is given ...

    Solution Summary

    Directional derivatives and tangent vectors are investigated. The proof or counterexample to disprove is determined.