Partial Derivatives

Question 1

What is a gradient?

Accepted Answer

Basically, it's the slope of a 3D figure

Question 2

One can use the 2nd partial derivative to find max/min of a 3d graph, similar to regular calc

Accepted Answer

True

Question 3

What is Multivariable Calculus?

Accepted Answer

Calculus... with multiple variables, Branch of calc where many variables are used instead of 1

Question 4

What is it called when a point has a negative divergence value?

Accepted Answer

Sink

Question 5

What were we teaching (specifically)?

Accepted Answer

Partial Derivatives

Question 6

How was this presentation?

Accepted Answer

Worst 54 minutes of my life, Interesting and cool, eh... i don't get it, I h a t e c a l c u l u s

Question 7

If a point has a positive divergence value, what is it called?

Accepted Answer

Source

Question 8

How can one denote a second derivative when there are multiple variables?

Accepted Answer

fxx

Question 9

In what ways can we apply partial derivatives and multivariable calculus in real life?

Accepted Answer

Finding maximum profit or minimum losses in businesses, Finding the way heat disperses through an object, Artificial Intelligence

Question 10

Calculus is hard

Accepted Answer

False, True

Question 11

What symbol are gradients denoted by?

Accepted Answer

∇

Question 12

Which of the following is NOT the correct way to denote a multivariable function?

Accepted Answer

f(x)

Question 13

Which of the following is another way to use vectors to represent the properties of a graph?

Accepted Answer

Curl

Question 14

Find fx of the function f(x,y) = 2x3 + 3xy2

Accepted Answer

fx = 6x2 + 3y2

Question 15

What's the main difference in the notation of regular derivatives versus partial derivatives?

Accepted Answer

"d" versus "∂", One's "d" and the other one looks like a flipped "6"

Question 16

Find fy of the function: f(x,y,z) = 3x3y2z + 2xy3

Accepted Answer

fy = 6x3zy+6xy2

Question 17

What theorem states that if the function is continuous, 2 of it's 2nd derivatives are identical

Accepted Answer

Schwarz’s theorem

Question 18

What must be true for a function to have a relative minimum in calculus?

Accepted Answer

f'(x) = 0 and f''(x) > 0

Questions 18