Derivatives

Question 1

intersects a a curve at one point

Answer 1

tangent line

Question 2

intersects a a curve at two points

Answer 2

secant line

Question 3

a line that mimics a curve at a particular region

Answer 3

tangent line

Question 4

a line that intersects a curve at two points

Answer 4

secant line

Question 5

if a limit exists, what is the slope of the tangent line

Answer 5

the limit itself

Question 6

if a limit is infinite, what is the tangent line?

Answer 6

the tangent line is vertical

Question 7

if the limit does not exist, the tangent line _____

Answer 7

does not exist as well

Question 8

the slope of the tangent line at x is the derivative of the function.

true or false?

Answer 8

true

Question 9

perpendicular to the tangent line

Answer 9

normal line

Question 10

how to compute for the slope of the normal line?

Answer 10

get the negative reciprocal of the slope of the tangent line

Question 11

if the slope of the tangent line is 0, what is the normal line?

Answer 11

the normal line is vertical

Question 12

if the function is constant, the derivative is ______

Answer 12

zero

Question 13

product rule mnemonic

Answer 13

derivative of left * right + left * derivative of right

or

dl * r + l *dr

Question 14

quotient rule mnemonic

Answer 14

low de high - high de low over low low

Question 15

chain rule mnemonic

Answer 15

derivative of the mommy function * derivative of the baby function

Question 16

if the derivative exists, is the function differentiable

Answer 16

yes

Question 17

all continuous functions are differentiable at all points

true or false?

Answer 17

false

Question 18

the left and right hand derivatives should be equal for the function to be differentiable

true or false?

Answer 18

true

Question 19

if the function is differentiable, the function is continuous

true or false?

Answer 19

true

Question 20

if f is not differentiable, then f is not continuous

true or false?

Answer 20

false

Question 21

y is not solely expressed in terms of x

Answer 21

implicit function

Question 22

y is isolated and is expressed in terms of x alone

Answer 22

explicit function

Question 23

all implicit functions can be expressed as an explicit function

true or false?

Answer 23

false