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5. Consider the function f(z, y) = sin(z² + y²). (a) direction of (4, 3). Find the derivative of f(z,y) at the point P(-v2,0, sin(2)) in the (b) On the same graph, include the gradient at point P. Sketch the level curve that goes through the point P(-/2,0, sin(2)). (c) point P(-V2,0, sin(2)). Find the direction in which the function f(1,y) has no change at the (d) What is the fastest rate of change possible at the pointP (-/2,0, sin(2))? (e) P(-v2,0, sin(2)). Find the equation of the line normal to the surface at the point

5. Consider the function f(z, y) = sin(z² + y²). (a) direction of (4, 3). Find the derivative of f(z,y) at the point P(-v2,0, sin(2)) in the (b) On the same graph, include the gradient at point P. Sketch the level curve that goes through the point P(-/2,0, sin(2)). (c) point P(-V2,0, sin(2)). Find the direction in which the function f(1,y) has no change at the (d) What is the fastest rate of change possible at the pointP (-/2,0, sin(2))? (e) P(-v2,0, sin(2)). Find the equation of the line normal to the surface at the point

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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Need help with parts C, D and E.

5. Consider the function f(r, y) = sin(r² + y²). (a) direction of (4, 3). Find the derivative of f(z,y) at the point P(-v2,0, sin(2)) in the (b) On the same graph, include the gradient at point P. Sketch the level curve that goes through the point P(-/2,0, sin(2)). (c) point P(-/2,0, sin(2)). Find the direction in which the function f(r, y) has no change at the (d) What is the fastest rate of change possible at the point (-v2,0, sin(2))? Find the equation of the line normal to the surface at the point (e) P(-v2,0, sin(2)).
Transcribed Image Text:5. Consider the function f(r, y) = sin(r² + y²). (a) direction of (4, 3). Find the derivative of f(z,y) at the point P(-v2,0, sin(2)) in the (b) On the same graph, include the gradient at point P. Sketch the level curve that goes through the point P(-/2,0, sin(2)). (c) point P(-/2,0, sin(2)). Find the direction in which the function f(r, y) has no change at the (d) What is the fastest rate of change possible at the point (-v2,0, sin(2))? Find the equation of the line normal to the surface at the point (e) P(-v2,0, sin(2)).
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