Given: F(x, y, z) = e²² + sin(4x + 6y − z) — - x ln(2y - 3) 3 and P(-3,2,0). (a) Find the rate of change of F at P in the direction of the vector from P to Q(0, 4, −6). (b) Find the unit vector in the direction where F decreases most rapidly at P. (c) Find an equation of the plane tangent to the surface S : F(x, y, z) = 1 at P.
Given: F(x, y, z) = e²² + sin(4x + 6y − z) — - x ln(2y - 3) 3 and P(-3,2,0). (a) Find the rate of change of F at P in the direction of the vector from P to Q(0, 4, −6). (b) Find the unit vector in the direction where F decreases most rapidly at P. (c) Find an equation of the plane tangent to the surface S : F(x, y, z) = 1 at P.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.3: Implicit Differentiation
Problem 44E
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Transcribed Image Text:Given: F(x, y, z) = e²² + sin(4x + 6y − z) —
x ln(2y - 3)
3
and P(-3,2,0).
(a) Find the rate of change of F at P in the direction of the vector from P to Q(0, 4, −6).
(b) Find the unit vector in the direction where F decreases most rapidly at P.
(c) Find an equation of the plane tangent to the surface S: F(x, y, z) = 1 at P.
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