If f(x, y, z) = 4zy", then the gradient at the point (5, 4, 5) is V f(5, 4, 5) =

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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If f(x, y, z) = 4zy, then the gradient at the point (5, 4, 5) is
V f(5, 4, 5) =
Transcribed Image Text:If f(x, y, z) = 4zy, then the gradient at the point (5, 4, 5) is V f(5, 4, 5) =
Jessica and Matthew are running toward the point P along the straight paths that make a fixed angle of 0 (Figure 1).
Suppose that Matthew runs with velocity va (m/s) and Jessica with velocity v, (m/s).
Let f(x, y) be the distance from Matthew to Jessica when Matthew is æ meters from P and Jessica is y meters from P.
P
B
FIGURE 1
Show that f(x, y) = Vx² + y² – 2xy cos 0.
• Assume that 0
= T/3. Use the Chain Rule to determine the rate at which the distance between Matthew and Jessica is changing when
28, y = 14, Va
4 m/s, and v,
4 m/s.
df
dt
Transcribed Image Text:Jessica and Matthew are running toward the point P along the straight paths that make a fixed angle of 0 (Figure 1). Suppose that Matthew runs with velocity va (m/s) and Jessica with velocity v, (m/s). Let f(x, y) be the distance from Matthew to Jessica when Matthew is æ meters from P and Jessica is y meters from P. P B FIGURE 1 Show that f(x, y) = Vx² + y² – 2xy cos 0. • Assume that 0 = T/3. Use the Chain Rule to determine the rate at which the distance between Matthew and Jessica is changing when 28, y = 14, Va 4 m/s, and v, 4 m/s. df dt
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