MATH 112 Exam 3 Memorization

Question 1

Rolle’s Theorem

Answer 1

Question 2

Area of a rectangle

Answer 2

Question 3

Where is the only place that a local min or max can happen?

Answer 3

critical number

Question 4

Second Derivative Test

Answer 4

Question 5

Increasing/Decreasing Test

Answer 5

Question 6

Perimeter of a rectangle

Answer 6

Question 7

Mean Value Theorem

Answer 7

Question 8

What is a critical number?

Answer 8

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 (e^x for example; e^x has NO critical numbers)

Question 9

Examples of indeterminate forms

Answer 9

Question 10

First Derivative Test

Answer 10

Question 11

ln(1/e) = ?

Answer 11

-1

Question 12

Volume of a cube

Answer 12

Question 13

Inflection Point

Answer 13

Question 14

Newton’s Method

Answer 14

Question 15

Area of a triangle

Answer 15

Question 16

Surface area of a cylinder

Answer 16

Question 17

What if f’(x_n) = 0?

Answer 17

There will be no x_n+1 approximation (can’t divide by zero)

Question 18

What’s the deal with similar triangles?

Answer 18

Question 19

Curve sketching process

Answer 19

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

Question 20

Circumference of a circle

Answer 20

Question 21

Surface area of a cube

Answer 21

Question 22

Area of a circle

Answer 22

Question 23

f’(a)=0

Is there necessarily an inflection point at a?

Answer 23

NO! You’d need more info.

Question 24

What is the square root of 1?

The square root of 2?

Answer 24

PLUS OR MINUS 1

PLUS OR MINUS THE SQUARE ROOT OF 2

Question 25

What is speed?

Answer 25

absolute value of velocity

Question 26

Surface area of a rectangular prism

Answer 26

Question 27

Concavity Test

Answer 27

Question 28

Volume of a cylinder

Answer 28

Question 29

What do you need to remember to do at the end of deriving a limit of a 0⁰ or 1^infinity indeterminate form?

Answer 29

REMEMBER THAT YOU SET IT EQUAL TO L

YOU THEREFORE HAVE ln(L)

YOU NEED TO SOLVE FOR L!!!

IT’S GONNA BE e^ans!!!!

Question 30

To use the special limit of sin…

Answer 30

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

Question 31

Volume of a rectangular prism

Answer 31

Question 32

Examples of functions that do NOT have local min or max values

Answer 32

• e^x
• 1/x
• arctan
• x^1/3
• x³

Generally have discontinuities or asymptotic behavior

Question 33

ln(e) = ?

Answer 33

1