Relating f, f', f''

Question 1

If f is increasing, then f’ is ________

Answer 1

positive

Question 2

If f is decreasing, then f’ is ________

Answer 2

negative

Question 3

If f has a maximum/minimum at an x value, then f’ at that x value equals ________ or is ________.

Answer 3

0, undefined

Question 4

If f is concave up, then f’ is ________

Answer 4

increasing

Question 5

If f is concave down, then f’ is ________

Answer 5

decreasing

Question 6

If f has a point of inflection at an x value, then f’ has a ________ ________ at that x value.

Answer 6

local extreme

Question 7

If f has a point of inflection at an x value, then f’’ is ________ or is ________, and ________ ________ at that x value.

Answer 7

0, undefined, changes sign

Question 8

If f’>0 on an interval then f is ________ on that interval.

Answer 8

increasing

Question 9

If f’<0 on an interval then f is ________ on that interval.

Answer 9

decreasing

Question 10

If f’‘>0 then f’ is ________ and f is ________

Answer 10

increasing, concave up

Question 11

If f’‘<0 then f’ is ________ and f is ________

Answer 11

decreasing, concave down

Question 12

If f’ has an x value that is equal to zero and f’’ at that x value is greater than zero, then a ________ occurs on f at that x value.

Answer 12

local min

Question 13

If f’ has an x value that is equal to zero and f’’ at that x value is greater than zero, then a ________ occurs on f at that x value.

Answer 13

local max