Go on. Explore!

lvl 0 • 0 xp

lvl 1

Home Market Decks Interests

AP Calculus AB Chapter 4

memorize.ai (lvl 286)

(0)

31 cards

()

Section 1

Preview this deck

how do you generally solve a related rates problem?

Front

1 / 31

Calculus Math

0.0

0 reviews

5			0
4			0
3			0
2			0
1			0

Active users

All-time users

Favorites

Last updated

6 years ago

Date created

Mar 1, 2020

Cards (31)

Section 1

(31 cards)

how do you generally solve a related rates problem?

Front

1. define what I need and what other rates I have 2. draw a picture 3. figure out the "general formula" 4. derive implicitly 5. substitute and solve 6. don't forget units.

Back

how do you find critical numbers?

Front

find when f'(x)=0 or when f'(x)=DNE

Back

in simplified terms, what is the second derivative test?

Front

1. find the points when f'(x)=0 2. plug those x values into f''(x) 3. f'' is positive then there is a local minimum and if f'' is negative then there local maximum

Back

what is an absolute minimum?

Front

the smallest value of f(x) in the domain of the function

Back

what are the absolute maximum and minimum considered to be?

Front

extreme values

Back

what is a local or relative maximum?

Front

the largest value of f(x) on some open interval in the domain of a function

Back

what is the extreme value theorem?

Front

if f is continuous over a closed interval, then fa has a maximum and minimum value over that interval

Back

what is Rolle's theorem?

Front

if f has a local maximum or minimum at c, and if f'(c) exists, then f'(c)=0

Back

when is f(x) decreasing?

Front

when f'(x) < 0

Back

how do you do la' hospital's rule?

Front

1. show that that the limit numerator and denominator separately equal what they need to equal 2. say "by la' hospital 3. show the limit of the derivative of the numerator over the derivative of the denominator 4. may have to do in more than once if it continues to not work

Back

what are the general steps for doing an optimization problem?

Front

1. figure out 'main' equation 2. make that equation in terms of one variable 3. derive 4. solve for minimum or maximum value by setting equal to 0 4. check with a sign chart

Back

how to solve a related rates problem that involves a cone?

Front

1. draw a labeled diagram of the cone 2. use similar triangle ratios and set equal in terms of r 3. derive the volume a cone formula 4. plug in and solve

Back

what is the second derivative test?

Front

-if f'(c)=0 and f''(c) is positive (concave up), then f has a local minimum at c -if f'(c)=0 and f''(c) is negative (concave down), then f has a local maximum at c

Back

when is f(x) concave down?

Front

when f''(x) < 0

Back

what are the steps of doing an optimization problem with distance and closest points?

Front

1. write distance formula 2. x1,y1 is the point is give you 3. x2,y2 is x, what y equals 4. plug in points 5. use calc to find zeros of derivative 6. plug zero in to original equation to find point

Back

when does f(x) have a local min?

Front

when f'(x) = 0 and when f'(x) changes from negative to positive

Back

what are local maximums and minimums considered to be?

Front

critical numbers because rolle's theorem states that if the slope of the local max. or min. exists then then the slope at that local max. or min equals 0

Back

what is an absolute maximum?

Front

the largest value of f(x) in the domain of the function

Back

what is the mean value theorem?

Front

if f is a differentiable (which also would make it continuous) function on the interval [a,b], then there exists a number c between a and b such that

Back

when does f(x) have a point of inflection?

Front

f(x) has an inflection point when f''(x) = 0 and when f''(x) changes sign

Back

what is the first derivative test?

Front

-if f' changes from positive to negative at c, then f has a local maximum at c -if f' changes from negative to positive at c, then f has a local minimum at c -if f' doesn't change sign at c, then f' has no local maximum or minimum

Back

what is a local or relative minimum?

Front

the smallest value of f(x) on some open interval in the domain of a function

Back

in simplified terms, what is the first derivative test?

Front

1. take the derivative of the function 2. find when f'(x)=0 3. use a sign chart to find the intervals of increase and decrease

Back

when can you solve a limit with la hospital's rule?

Front

when the limits of both the numerator and denominator equal 0, negative infinity, or positive infinity when the limit of the numerator is equal to the limit of only the denominator (with indeterminate forms)

Back

how do you find absolute maximum and minimum?

Front

1. find the coordinates of the endpoints 2. find the coordinates of the local maximums and minimums 3. decide absolute maximum and minimum

Back

what is a critical number?

Front

a number c in the domain of f such that either f'(c) = 0 or f'(c) does not exist

Back

when is f(x) increasing?

Front

when f'(x) > 0

Back

what are indeterminate forms?

Front

limits that may or may not exist

Back

when does f(x) have a local max?

Front

when f'(x) = 0 and when f'(x) changes from positive to negative

Back

when is f(x) concave up?

Front

when f''(x) > 0

Back

how do you find the absolute max and absolute min?

Front

plug in the local max and local min to original equation to see which local max has largest f(x) value and which local min has smallest f(x) value

Back