MATH 112 Exam 3 Memorization Flashcards
Rolle’s Theorem
Area of a rectangle
Where is the only place that a local min or max can happen?
critical number
Second Derivative Test
Increasing/Decreasing Test
Perimeter of a rectangle
Mean Value Theorem
What is a critical number?
A critical number is a number a IN THE DOMAIN of f such that f’(a) = 0 or f’(a) is undefined (i.e., a is not in the domain of f’)
Note that a MUST be in the domain of f but does NOT have to be in the domain of f’
There are functions that DO NOT have critical numbers (ex for example; ex has NO critical numbers)
Examples of indeterminate forms
First Derivative Test
ln(1/e) = ?
-1
Volume of a cube
Inflection Point
Newton’s Method
Area of a triangle
Surface area of a cylinder
What if f’(xn) = 0?
There will be no xn+1 approximation (can’t divide by zero)
What’s the deal with similar triangles?
Curve sketching process
Domain
Intercepts
Y-intercept if f(0)
X-intercept set y = 0 and solve for x
Symmetry
See whether f(-x)=f(x); if so, the function is even
If f(-x)=-f(x), the function is odd
Asymptotes
Check behavior at VA from both sides!!
Intervals of Inc/Dec
Local Max/Min
Concavity and Points of Inflection
Circumference of a circle
Surface area of a cube
Area of a circle
f’(a)=0
Is there necessarily an inflection point at a?
NO! You’d need more info.
What is the square root of 1?
The square root of 2?
PLUS OR MINUS 1
PLUS OR MINUS THE SQUARE ROOT OF 2
What is speed?
absolute value of velocity
Surface area of a rectangular prism
Concavity Test
Volume of a cylinder
What do you need to remember to do at the end of deriving a limit of a 00 or 1infinity indeterminate form?
REMEMBER THAT YOU SET IT EQUAL TO L
YOU THEREFORE HAVE ln(L)
YOU NEED TO SOLVE FOR L!!!
IT’S GONNA BE eans!!!!
To use the special limit of sin…
The thing in the argument of sin MUST be going to 0!!!
Or you must be evaluating the limit of the function as x approaches 0
Volume of a rectangular prism
Examples of functions that do NOT have local min or max values
- ex
- 1/x
- arctan
- x1/3
- x3
Generally have discontinuities or asymptotic behavior
ln(e) = ?
1
