Show that the directional derivative of f(x, y, z) = z²x + y3 at (6, 9, 8) in the direction. √5 To find the directional derivative of f, we first need the gradient of fat (6, 9, 8). This is equal to This product is jis 110 5. . Therefore, the directional derivative of f(x, y, z) = z²x + y3 in the direction of . Next, we take the ---Select--- (5) + (5) is 110√/5. of this vector and the vector (7/5)³ + (735)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1
Show that the directional derivative of f(x, y, z) = z²x + y³ at (6, 9, 8) in the direction
(√5)
To find the directional derivative of f, we first need the gradient of fat (6, 9, 8). This is equal to
This product is
+
2
(75)³1
j is 110√5.
Therefore, the directional derivative of f(x, y, z) = z²x + y³ in the direction of
Next, we take the ---Select---
1
2
(7/5)² + ( 7²/5)³₁
i
j is 110√5.
✓of this vector and the vector
1
2
( √5)² + (7/5)³¹.
Transcribed Image Text:1 Show that the directional derivative of f(x, y, z) = z²x + y³ at (6, 9, 8) in the direction (√5) To find the directional derivative of f, we first need the gradient of fat (6, 9, 8). This is equal to This product is + 2 (75)³1 j is 110√5. Therefore, the directional derivative of f(x, y, z) = z²x + y³ in the direction of Next, we take the ---Select--- 1 2 (7/5)² + ( 7²/5)³₁ i j is 110√5. ✓of this vector and the vector 1 2 ( √5)² + (7/5)³¹.
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