1. Find the critical points of f (x,y) = 8y³ + x³ – 6xy and use the second derivative test to classify them as local minima, local maxima, or saddle points. %3D 2. Find the linearization of g(x, y, z) = In(x²y²z²) at the point P (;,72). 3. a) Find the derivative of f (x, y) = 2x + e-(x*+y*) – cos(xy) + 7 in the direction parallel to v = (-3, v7) at the point Q(0,-1). %3D b) In what direction does f decrease most rapidly at Q(0,-1)? 4. The position vector of a particle is given as 7(t) = (et – 17,2e-t + 2n, 100 – 2t). At what time or times (if any) are the particle's velocity and acceleration vectors perpendicular to one another? 5. If z = cos(xy) + ycos(x) and x = u² – v, and y = u + v² , use the Chain Rule %3D az to find and . av' ди 6. Evaluate the double integral: S,* S +dydx y
1. Find the critical points of f (x,y) = 8y³ + x³ – 6xy and use the second derivative test to classify them as local minima, local maxima, or saddle points. %3D 2. Find the linearization of g(x, y, z) = In(x²y²z²) at the point P (;,72). 3. a) Find the derivative of f (x, y) = 2x + e-(x*+y*) – cos(xy) + 7 in the direction parallel to v = (-3, v7) at the point Q(0,-1). %3D b) In what direction does f decrease most rapidly at Q(0,-1)? 4. The position vector of a particle is given as 7(t) = (et – 17,2e-t + 2n, 100 – 2t). At what time or times (if any) are the particle's velocity and acceleration vectors perpendicular to one another? 5. If z = cos(xy) + ycos(x) and x = u² – v, and y = u + v² , use the Chain Rule %3D az to find and . av' ди 6. Evaluate the double integral: S,* S +dydx y
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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Transcribed Image Text:1. Find the critical points of f (x, y) = 8y³ + x³ – 6xy and use the second
derivative test to classify them as local minima, local maxima, or saddle
points.
2. Find the linearization of g(x, y, z) = In(x²y²z²) at the point P (,72).
3. a) Find the derivative of f (x, y) = 2x + e-(x²+y“) – cos(xy) + 7 in the
direction parallel to i = (-3, v7) at the point Q(0,-1).
b) In what direction does f decrease most rapidly at Q(0,-1)?
4. The position vector of a particle is given as 7(t) = (et – 17, 2e-t + 27, 100 – 2t).
At what time or times (if any) are the particle's velocity and acceleration
vectors perpendicular to one another?
5. If z = cos(xy) + ycos(x) and x = u? – v, and y = u + v² , use the Chain Rule
%3D
əz
az
and
dv'
to find
ди
6. Evaluate the double integral: " S+2dydx
y
7. Find the points on the sphere x2 + y2 + z² = 1 where the tangent plane is parallel
to the plane 3x + 2y – z = 1.
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