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x² Consider the function f(x,y)=1-- whose graph is a paraboloid (see figure). a. Find the value of the directional derivative at the point (3,0) in the direction (-1/2 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.) √2 √2 2

x² Consider the function f(x,y)=1-- whose graph is a paraboloid (see figure). a. Find the value of the directional derivative at the point (3,0) in the direction (-1/2 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.) √2 √2 2

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 13E
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x² Consider the function f(x,y)=1-2 whose graph is a paraboloid (see figure). a. Find the value of the directional derivative at the point (3,0) in the direction (-1/2 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.) √2 √2 2
Transcribed Image Text:x² Consider the function f(x,y)=1-2 whose graph is a paraboloid (see figure). a. Find the value of the directional derivative at the point (3,0) in the direction (-1/2 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.) √2 √2 2
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