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4. Suppose that the following information about a function f is known. It has continuous partial derivatives. From point (0,0) in the direction of point (3, 4), the directional derivative is known to be 2. From point (0,0) in the direction of point (5, 12), the directional derivative is determined to be 5. Determine the gradient of the function at the origin, and approximate (to two decimal places) the direction in which the directional derivative is most negative. (This is an example of the core step of the method of gradient descent, which is widely used to numerically approximate the location of critical points.)

4. Suppose that the following information about a function f is known. It has continuous partial derivatives. From point (0,0) in the direction of point (3, 4), the directional derivative is known to be 2. From point (0,0) in the direction of point (5, 12), the directional derivative is determined to be 5. Determine the gradient of the function at the origin, and approximate (to two decimal places) the direction in which the directional derivative is most negative. (This is an example of the core step of the method of gradient descent, which is widely used to numerically approximate the location of critical points.)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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4. Suppose that the following information about a function f is known. It has continuous partial derivatives. From point (0,0) in the direction of point (3, 4), the directional derivative is known to be 2. From point (0,0) in the direction of point (5, 12), the directional derivative is determined to be 5. Determine the gradient of the function at the origin, and approximate (to two decimal places) the direction in which the directional derivative is most negative. (This is an example of the core step of the method of gradient descent, which is widely used to numerically approximate the location of critical points.)
Transcribed Image Text:4. Suppose that the following information about a function f is known. It has continuous partial derivatives. From point (0,0) in the direction of point (3, 4), the directional derivative is known to be 2. From point (0,0) in the direction of point (5, 12), the directional derivative is determined to be 5. Determine the gradient of the function at the origin, and approximate (to two decimal places) the direction in which the directional derivative is most negative. (This is an example of the core step of the method of gradient descent, which is widely used to numerically approximate the location of critical points.)
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