Let f: R² → R be a differentiable function. (a) At the point (ro. Yo) = (1,5), it is known that the equation of the tangent plane to the surface z = f(x, y) is -2x+3y-z = 17. Find the directional derivative of f at the point (1,5) in the direction towards the origin.
Let f: R² → R be a differentiable function. (a) At the point (ro. Yo) = (1,5), it is known that the equation of the tangent plane to the surface z = f(x, y) is -2x+3y-z = 17. Find the directional derivative of f at the point (1,5) in the direction towards the origin.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let f: R2R be a differentiable function.
(a) At the point (ro, yo) = (1,5), it is known that the equation of the tangent plane to the
surface z=f(x, y) is
-2x+3y-z = 17.
Find the directional derivative of f at the point (1,5) in the direction towards the origin.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1e65d3f-3c77-4e7f-88fc-bf17213b1ce1%2F249df3cb-259f-4ce2-a424-50ac4546fc86%2Fo9d2ra9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let f: R2R be a differentiable function.
(a) At the point (ro, yo) = (1,5), it is known that the equation of the tangent plane to the
surface z=f(x, y) is
-2x+3y-z = 17.
Find the directional derivative of f at the point (1,5) in the direction towards the origin.
![(b) At the point (x, y) = (2022,-7), it is known that the directional derivative of f is zero
in the direction = π/4, and the directional derivative of f in the direction = -π/4
is -8, where and are angles measured anticlockwise from the positive x axis.
Find Vf|(2022,-7)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1e65d3f-3c77-4e7f-88fc-bf17213b1ce1%2F249df3cb-259f-4ce2-a424-50ac4546fc86%2Fnpxdaq5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(b) At the point (x, y) = (2022,-7), it is known that the directional derivative of f is zero
in the direction = π/4, and the directional derivative of f in the direction = -π/4
is -8, where and are angles measured anticlockwise from the positive x axis.
Find Vf|(2022,-7)
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