Exam 1 Flashcards
Functions, Graphs, Limits, Intro to Derivatives
How to evaluate piecewise functions
Choose the part of the rule that applies for the given input; not all of the rules
Average cost formula
C(x)/x
Total Profit
(profit/item)(number of items sold)
Profit
Revenue - Cost
How can you get the vertex of a graph?
-b/2a
What does profit as a function of price mean?
(profit/units)(number of units)
Slope rules for parallel and perpendicular lines
Parallel - same slope
Perpendicular - negative reciprocal
Profit function given retail question
(x +/- cost of item) (number sold now + (current price - x)(how many more units will be sold)
Volume/Surface Area/Area/Perimeter problem function format
Write the volume/area/SA/perimeter formulas. Substitute one equation into the other
Directly proportionality
y = kx
Inverse proportionality
y = k/x
Joint proportionality
y = kxv
How to find market equilibrium
Set S(x) and D(x) equal to each other and solve. Put x into the equation to solve for price
How do get break even?
Set both equation equal to each other and solve for x
Rule for a limit to exist
Must come together at the same y value
How do you evaluate a limit algebriacally
Substitute the x -> number into x
limit 0/0
indeterminate
limit nonzero/0
find vertical asymptote
What does x-9 / √x-3 equal?
(√x+3)(√x-3)/(√x-3)
If the degree of the denominator of a function is higher then …
The limit equals 0
How can you evaluate a limit where x approaches infinity?
Find the vertical asymptote
How do you evaluate a piecewise function for continuity?
Evaluate the limit algebriacally; if the rules do not equal each other then the function is not continuous at x
When is x continuous?
All real numbers except what makes the denominator zero or a square root negative
How can you find a derivative using the definition of the derivative?
[f(x+h) - f(x)] / h
Substitute the function into x and solve for x = number
How can you find the equation of the tangent line?
Find the derivative, and solve for x, which equals the slope
The (x,y) is the x = number, and the y = input x into the original function
How can you find the max/min using derivatives?
Solve the derivative for x
Power rule
(x to n) = nx to the n-1
Percentage formula
100 x [d’(x)/d(x)]
What does it mean by how much something will change during the sixth year?
C(6) - C(5)
Product rule
[f(x)g(x)]’ = f’(x)g(x) + f(x)g’(x)
Quotient rule
[f(x)/g(x)] = [f’(x)g(x) - f(x)g’(x)] / [g(x)] squared
What does the “rate of efficiency changing with respect to something” mean?
Take the second derivative
What does “long run” mean?
Take the limit
