Differentiation and Integration Flashcards
1
Q
Limit definition of differentiation
A
f(x+h) - f(x) / h
2
Q
Product Rule (Differentiation)
A
f’g + g’f
3
Q
Quotient Rule (Differentiation)
A
(f’g - g’f) / g^2
4
Q
Concave Up
A
Second derivative > 0, Minimum
5
Q
Concave Down
A
Second derivative < 0, Maximum
6
Q
Critical Point
A
Derivative = 0, or Function is not differentiable
7
Q
Stationary Point
A
Derivative = 0, Is a critical point
8
Q
Point of Inflection
A
Function is Continuous and concavity changes about a point
9
Q
Integration by Parts
A
Integral of g’(x)f(x) = f(x)g(x) - integral of f’(x)g(x)
10
Q
Functions of Two Variables
A
Rearrange to Z = rest of equation. Find axis intercepts by making all other variables = 0.
11
Q
Partial Derivatives with respect to x/y/z
A
Treat the other variables as constants
