Rules Learned in Calc I
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
|
|
||||
|---|---|---|---|---|---|
| If f is ____ on the closed interval [a,b], then f attains ___ and ___ in [a,b] | continuous, absolute max, absolute min
🗑
|
||||
| f(x) has an inflection point at x=c if ___. | f changes concavity at c.
🗑
|
||||
| f(x) has a critical point at x=c, if ___ or ___. | f'(c)=0 or DNE
🗑
|
||||
| If f'(x) is greater than 0 on Interval I, then f is ___. | increasing on I
🗑
|
||||
| If f'(x) is less than 0 on interval I, then f is ___. | decreasing on I
🗑
|
||||
| If f''(x) is less than 0 on Interval I, then f'(x) is ___ and f is ___. | decreasing, concave down
🗑
|
||||
| If f''(x) is greater than 0 on Interval I, then f'(x) is ___ and f is ___. | increasing, concave up
🗑
|
||||
| x=c is an inflection point if ___. | the concavity changes
🗑
|
||||
| f(c) is an absolute max on I if ___. | f(c) is greater than f(x) for all values x in I.
🗑
|
||||
| f(c) is an absolute min on I if ___. | f(c) is less then f(x) for all values x in I.
🗑
|
||||
| f(c) is a local max if ___. | f(c) is greater than f(x) for all x near c.
🗑
|
||||
| f(c) is a local min if ___. | f(c) is less than f(x) for all x near c.
🗑
|
||||
| Assume that c is a critical point of f and that f is continuous at x=c. 1. If f'(x) changes from positive to negative, then c is ___. 2. If f'(x) changes from negative to positive, then c is ___. 3. If f'(x) does not change sign, then c is ___. | 1. Local max
2. Local min
3. Neither local max nor local min
🗑
|
||||
| Assume f'' is continuous near c. 1. If f''(c) is greater than 0, then f(c) is ___. 2. If f''(c) is less than 0, then f(c) is ___. | 1. Local max
2. Local min
🗑
|
||||
| If f is ___ on a closed interval (a,b), then there exists a c in (a,b), such that ___. | continuous, f'(c)=f(b)-f(a)/b-a
🗑
|
||||
| If f and g are ___ and ___ near a, and the limit of f(x)/g(x) as x approaches a gives an indeterminate form of ___ or ___, then ___. | continuous, g does not equal 0, infinity/infinity. 0/0, limit as x approaches a is f'(x)/g'(x)
🗑
|
||||
| A function f is continuous at a number a if ___. | The limit of f(x) as x approaches a = f(a)
🗑
|
||||
| Suppose that f is ___ on the closed interval [a,b] and let N be any number between f(a) and f(b) where ___. Then there exists a number c in (a,b), such that ___. | continuous, f(a) does not equal f(b), f(c)=N
🗑
|
||||
| The line x=a is a vertical asymptote when ___. | The limit of f(x) as x approaches a is infinity or negative infinity.
🗑
|
Review the information in the table. When you are ready to quiz yourself you can hide individual columns or the entire table. Then you can click on the empty cells to reveal the answer. Try to recall what will be displayed before clicking the empty cell.
To hide a column, click on the column name.
To hide the entire table, click on the "Hide All" button.
You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
To hide a column, click on the column name.
To hide the entire table, click on the "Hide All" button.
You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.
Normal Size Small Size show me how
Normal Size Small Size show me how
Created by:
100000465038020
Popular Math sets