Let f(x, y) = sih(x) + cas (y), v=<-1₁17₁ and P= (0, 1) Let u be a unit vector in the direction of vi Select ALL that are true A. The derivative of f in the direction of v at P is positive: DufCP) >0. B. The maximum rate of change of f at P is in the direction v = (-1₁1), c. The maximum rate of change of f at P is in the direction -V= (1₁-1), The maximum rate of change of fat P is in the direction of Df (P), enough in formation to determine the maximum rate of change of fat P. Ei We do not have
Let f(x, y) = sih(x) + cas (y), v=<-1₁17₁ and P= (0, 1) Let u be a unit vector in the direction of vi Select ALL that are true A. The derivative of f in the direction of v at P is positive: DufCP) >0. B. The maximum rate of change of f at P is in the direction v = (-1₁1), c. The maximum rate of change of f at P is in the direction -V= (1₁-1), The maximum rate of change of fat P is in the direction of Df (P), enough in formation to determine the maximum rate of change of fat P. Ei We do not have
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Let \( f(x,y) = \sin(x) + \cos(y) \), \( v = \langle -1, 1 \rangle \), and \( P = \left( 0, \frac{\pi}{2} \right) \).
Let \( u \) be a unit vector in the direction of \( v \).
Select ALL that are true:
A. The derivative of \( f \) in the direction of \( v \) at \( P \) is positive: \( D_u f(P) > 0 \).
B. The maximum rate of change of \( f \) at \( P \) is in the direction \( v = \langle -1, 1 \rangle \).
C. The maximum rate of change of \( f \) at \( P \) is in the direction \(-v = \langle 1, -1 \rangle \).
D. The maximum rate of change of \( f \) at \( P \) is in the direction of \(\nabla f(P)\).
E. We do not have enough information to determine the maximum rate of change of \( f \) at \( P \).
Expert Solution
Step 1: Explanation
Let us solve above problem
Step by step
Solved in 3 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
