Multivariable Calculus: Space Figures & Partial Derivatives Test Review

Question 1

A gradient at a point will behave how relative to a level curve?

Accepted Answer

perpendicular

Question 2

The directional derivative of z = (x2)(e-y) at the point (-1,0) in the direction of (4,-3) is

Accepted Answer

-1

Question 3

Which equation below gives the graph of this quadric surface?

Accepted Answer

4x2- y2 - z + 8x + 8z + 24 = 0

Question 4

See question...

Accepted Answer

16 and 8

Question 5

A gradient points in what direction?

Accepted Answer

maximum rate of change

Question 6

Given f(x,y) below and x = sin(2t) and y = cos t, find df/dt when t = 0.

Accepted Answer

6

Question 7

Clairaut's Theorem states that _____

Accepted Answer

fxy = fyx

Question 8

∇f(x, y), where f(x, y) = 10x5y is

Accepted Answer

<50x4y, 10x5>

Question 9

A gradient is a(n) _____

Accepted Answer

vector

Question 10

Find the domain & range of f(x,y,z) = √(4 - x2-y2-z2).

Accepted Answer

x2+y2+y2 ≤ 4, 0 ≤ w ≤ 2

Question 11

The "D" in the multivariable second derivative test is:

Accepted Answer

fxxfyy - (fxy)2

Question 12

If fxxfyy - (fxy)2 < 0, this means . . .

Accepted Answer

saddle point

Question 13

Find the equation of the tangent plane to the surface z + 7 = xey cos(z) at the point (7,0,0).

Accepted Answer

x + 7y - z = 7

Question 14

Is fxy at P positive or negative?

Accepted Answer

positive

Question 15

At what pt. does the following function have a local max: f(x,y) = 3 - 10x + 12y - 5x2 - 6y2

Accepted Answer

(-1,1)

Question 16

Given f(x, y, z) = x30y26z, what is fxyzyzzyyxx?

Accepted Answer

0

Question 17

A PringleTM is an example of a(n) _____

Accepted Answer

all of the above

Question 18

Find the equation of the tangent plane to f(x,y) = (ex)(cos y) at the point (0,0,1).

Accepted Answer

z = x + 1

Questions 18