# Advanced Calculus: The Mean Value Theorem and Directional Derivatives

Not what you're looking for?

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.

##### Purchase this Solution

##### Solution Summary

A proof involving directional derivatives is provided. The solution is detailed.

##### Solution Preview

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 ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts