Solved: Direction of steepest ascent and descent Consider

Chapter 11, Problem 21E

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QUESTION:

Direction of steepest ascent and descent Consider the following functions and points P.

a. Find the unit vectors that give the direction of steepest ascent and steepest descent at P.

b. Find a vector that points in a direction of no change in the function at P.

\(f(x, y)=x^{2}-4 y^{2}-9 ; P(1,-2)\)

Questions & Answers

QUESTION:

Direction of steepest ascent and descent Consider the following functions and points P.

a. Find the unit vectors that give the direction of steepest ascent and steepest descent at P.

b. Find a vector that points in a direction of no change in the function at P.

\(f(x, y)=x^{2}-4 y^{2}-9 ; P(1,-2)\)

ANSWER:

Solution 21EStep 1 of 4:In this problem we need to find the unit vectors that gives the steepest ascent and steepest descent at P.1. Find the unit vectors that gives the steepest ascent and steepest descent at P.Given: The steepest ascent and steepest descent of a function can be obtained by finding its gradient at the points respectively.let us find gradient where is given by

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