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Find the unit vector in the direction in which f (x,y) =x+ sin(x + 2 ·y) increases most rapidly at P= (0,0) and give the rate of change of f in that direction. Find the unit vector in the direction in which f decreases most rapidly at P and give the rate of change of f in that direction. The unit vector in the direction in which f increases most rapidly at P is + . The rate of change in that direction is The unit vector in the direction in which f decreases most rapidly at P is The rate of change in that direction is +.

Find the unit vector in the direction in which f (x,y) =x+ sin(x + 2 ·y) increases most rapidly at P= (0,0) and give the rate of change of f in that direction. Find the unit vector in the direction in which f decreases most rapidly at P and give the rate of change of f in that direction. The unit vector in the direction in which f increases most rapidly at P is + . The rate of change in that direction is The unit vector in the direction in which f decreases most rapidly at P is The rate of change in that direction is +.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section3.3: Vectors In The Plane
Problem 11ECP
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Find the unit vector in the direction in which f (x,y) =x + sin (x + 2.y) increases most rapidly at P= (0,0) and give the rate of change of f in that direction. Find the unit vector in the direction in which f decreases most rapidly at P and give the rate of change of f in that direction. The unit vector in the direction in which f increases most rapidly at P is + . The rate of change in that direction is + The unit vector in the direction in which f decreases most rapidly at P is + . The rate of change in that direction is +
Transcribed Image Text:Find the unit vector in the direction in which f (x,y) =x + sin (x + 2.y) increases most rapidly at P= (0,0) and give the rate of change of f in that direction. Find the unit vector in the direction in which f decreases most rapidly at P and give the rate of change of f in that direction. The unit vector in the direction in which f increases most rapidly at P is + . The rate of change in that direction is + The unit vector in the direction in which f decreases most rapidly at P is + . The rate of change in that direction is +
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