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Consider the function f(x.y) = 2 –-y, whose graph is a paraboloid (see figure). a. Find the value of the directional derivative at the point (0,3) in the direction 2 2

Consider the function f(x.y) = 2 –-y, whose graph is a paraboloid (see figure). a. Find the value of the directional derivative at the point (0,3) in the direction 2 2

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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Consider the function f(x,y) = 2 --y, whose graph is a paraboloid (see figure). 3 V2 V2 a. Find the value of the directional derivative at the point (0,3) in the direction 2 b. Sketch the level curve through the given point and indicate the direction of the directional derivative from part (a). a. The directional derivative is (Type an exact answer, using radicals as needed.) b. Choose the correct sketch below. O A. В. C. D. X 10 40
Transcribed Image Text:Consider the function f(x,y) = 2 --y, whose graph is a paraboloid (see figure). 3 V2 V2 a. Find the value of the directional derivative at the point (0,3) in the direction 2 b. Sketch the level curve through the given point and indicate the direction of the directional derivative from part (a). a. The directional derivative is (Type an exact answer, using radicals as needed.) b. Choose the correct sketch below. O A. В. C. D. X 10 40
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