Deck 14: Partial Derivatives

Question 1

Answer 1

Question 2

Answer 2

Question 3

Answer 3

Question 4

Question 5

Question 6

Question 7

Find three positive real numbers whose sum is 388 and whose product is as large as possible.

Question 8

Find all the second partial derivatives.

Question 9

Question 10

Question 11

Find the first partial derivatives of the function.

Question 12

Question 13

Find the differential of the function.

Question 14

Find the local maximum, and minimum value and saddle points of the function.

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Find the equation of the normal line to the given surface at the specified point.

Question 21

Question 22

A boundary stripe 2 in.wide is painted around a rectangle whose dimensions are 100 ft by 240 ft. Use differentials to approximate the number of square feet of paint in the stripe.

Question 23

Question 24

Question 25

Find the indicated partial derivative.

Question 26

Question 27

Question 28

Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01
Cm thick.(rounded to the nearest hundredth.)

Question 29

Question 30

Find equations for the tangent plane and the normal line to the surface with equation

Question 31

Question 32

Question 33

Question 34

Question 35

Question 36

Question 37

Question 38

Question 39