Unit 4 - Contextual Application of Differentiation

Question 1

If f’(x) > 0, then the function is

Answer 1

increasing

Question 2

If f’(x) < 0, then the function is

Answer 2

decreasing

Question 3

Position function

Answer 3

represents position of an object

often notated as s(t) where t is time

Question 4

Velocity function

Answer 4

represents velocity of an object

v(t) = s’(t)

Question 5

Acceleration function

Answer 5

represents acceleration of an object

a(t) = v’(t)

Question 6

Velocity

Answer 6

Rate of change of position

Question 7

If v(t) < 0, then the particle is

Answer 7

Moving left (x-axis)
Moving down (y-axis)

Question 8

If v(t) > 0, then the particle is

Answer 8

Moving right (x-axis)
Moving up (y-axis)

Question 9

If v(t) = 0, then the particle is

Answer 9

at rest/ not moving

Question 10

Avg velocity

Answer 10

s(b) - s(a) / b-a on interval [a, b]

Question 11

Speed

Answer 11

|velocity|

Question 12

If velocity and acceleration has the same sign, then the particle is

Answer 12

Speeding up

Question 13

If velocity and acceleration has different sign, then the particle is

Answer 13

Slowing down

Question 14

Displacement

Answer 14

Net change in position

Initial position - final position

Question 15

To know if something is increasing or decreasing,

Answer 15

Check its derivative

Question 16

If the sign of derivative is greater than zero, then

Answer 16

the function is increasing

Question 17

If the sign of derivative is less than zero, then

Answer 17

the function is decreasing

Question 18

Related rates

Answer 18

Changing dimensions relate to each other

Differentiate relationship to one variable

Question 19

To solve a related rates problem

Answer 19

1- Draw a picture
2 - Make list of all known and unknown rates and quantities
3- relate variables in an equation
4 - Differentiate with respect to time
5- Substitute know quantities & rates and solve

Question 20

Substituting non-constant quantity before differentiating is

Answer 20

NOT ALLOWED

Question 21

If a function is concave up, the points on a tangent line would be

Answer 21

Underestimate

Question 22

If a function is concave down, the points on a tangent line would be

Answer 22

Overestimate

Question 23

L’Hopital Rule

Answer 23

Suppose f(a)=0 and g(a)=0 and lim f(x) / g(x) = 0/0 or infinity/ infinity x->a
Then, lim f(x) / g(x) = f’(a) / g’(a)
x->a

Question 24

The derivative of a function can be interpreted

as the

Answer 24

instantaneous rate of change with respect to its independent variable.

Question 25

The unit for f ‘(x) is the

Answer 25

unit for f divided by the unit for x.