Test 3

Question 1

What is chain rule?

Answer 1

partialX(fullX) + partialY(fullY)

Question 2

How do you calculate directional derivative?

Answer 2

gradient * unit vector

Question 3

calculate gradient vector

Answer 3

< fx, fy, fz >

Question 4

how to find cps

Answer 4

find derivative in terms of each component, find values where each variable = 0, make pts

Question 5

find local max and mins

Answer 5

1. calculate fxx, fyy, fxy
2. get d, fxx*fyy - (fxy)^2
3. mins –> d>0, fxx>0
4. max –> d>0, fxx<0
5. if d<0, saddle pt
6. d = 0, inconclusive

Question 6

find absolute max and min (with constraint)

Answer 6

check edges and corners
fx = lambda*gx
fy = lambda*gy
fz = lambda*gz
use constraint to find x, y, z
sub into original to find abs max and min

Question 7

IBP formula

Answer 7

uv - int(vdu)

Question 8

find partial dz/dx (x,y,z)

Answer 8

-Fx/Fz

Question 9

questions with t

Answer 9

partialzxfullx + partialzyfully

Question 10

tangent plane

Answer 10

gradient dot < x - xo, y - yo >

Question 11

direction of max inc/dec

Answer 11

grad(f) |

Question 12

tangent plane equation for level surface

Answer 12

derivative of each component, plug in point for slope

plug into plane equation

Question 13

normal line for level surface

Answer 13

get slope, plug into parametric

Question 14

find abs max/min given ranges

Answer 14

find fx and fy, solve for x and y

check edges, plug in value one at a time, get derivative, these become points

Question 15

sketch position vector and tangent vecter at pt

Answer 15

plug in point and draw vector, take deriv and plug in

Question 16

dy/dx =

Answer 16

-Fx / Fy