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f(x, y) = 5e cosy, (a,b) = (0, 1), П and v = (2, 3). a. Calculate the directional derivative of f at the point (a, b) in the direction defined by v. 4 P b. Find the direction at (a, b) in which the rate of change of f is greatest. c. Find the maximum rate of change. d. Fill in the blank: f decreases the most at (a, b) in the direction of

f(x, y) = 5e cosy, (a,b) = (0, 1), П and v = (2, 3). a. Calculate the directional derivative of f at the point (a, b) in the direction defined by v. 4 P b. Find the direction at (a, b) in which the rate of change of f is greatest. c. Find the maximum rate of change. d. Fill in the blank: f decreases the most at (a, b) in the direction of

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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f(x, y) = 5e cosy, (a,b) = (0, 1), П and v = (2, 3). a. Calculate the directional derivative of f at the point (a, b) in the direction defined by v. 4 P b. Find the direction at (a, b) in which the rate of change of f is greatest. c. Find the maximum rate of change. d. Fill in the blank: f decreases the most at (a, b) in the direction of
Transcribed Image Text:f(x, y) = 5e cosy, (a,b) = (0, 1), П and v = (2, 3). a. Calculate the directional derivative of f at the point (a, b) in the direction defined by v. 4 P b. Find the direction at (a, b) in which the rate of change of f is greatest. c. Find the maximum rate of change. d. Fill in the blank: f decreases the most at (a, b) in the direction of
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