Question

Suppose f is a function giving the altitude (height above ground) in feet of a small plane, depending on time t in seconds.

Select the best interpretation of each value, function, or expression below.

(a) f(50)=1000 means

the altitude of the plane is 1000 feet after 50 secondsthe altitude of the plane is increasing at a rate of 50 feet per second after 1000 seconds    the altitude of the plane is 50 feet after 1000 secondsthe altitude of the plane is increasing at a rate of 1000 feet per second after 50 seconds

(b) f'(1000)=50 means

the altitude of the plane is increasing at a rate of 50 feet per second after 1000 secondsthe altitude of the plane is 50 feet after 1000 seconds    the altitude of the plane is 1000 feet after 50 secondsthe altitude of the plane is increasing at a rate of 1000 feet per second after 50 seconds

(c)

f(1000)−f(0)

1000−0

= 50 means

the plane's speed increased an average of 50 feet per second over 1000 seconds the plane's altitude increased 50 feet per second for 1000 seconds     the plane's altitude increased an average of 50 feet per second over 1000 seconds the plane's speed increased 50 feet per second for 1000 seconds

(d)

1

1000

1000	f(t)dt
0

is the plane's

average altitude over 1000 seconds, in feetinstantaneous rate of change in altitude after 1000 seconds, in feet per second    average rate of change in altitude over 1000 seconds, in feet per second

(e)

d

dx

x	f(t)dt
0

is the plane's

average altitude function, in feetaverage speed function, in feet per second     instantaneous rate of change in altitude, in feet per secondaverage velocity function, in feet per second

(f)

1000	f'(t)dt
0

= 50 means

the net change in the speed of the plane over 1000 seconds is 50 feet per secondthe average change in the speed of the plane over 1000 seconds is 50 feet per second    the average change in the altitude of the plane over 1000 seconds is 50 feet the net change in the altitude of the plane over 1000 seconds is 50 feetthe instantaneous change in the altitude of the plane at 1000 seconds is 50 feetthe instantaneous change in the speed of the plane at 1000 seconds is 50 feet per second

Answer 1

(a) f(50)=1000 means

the altitude of the plane is 1000 feet after 50 seconds

(b) f'(1000)=50 means

the altitude of the plane is increasing at a rate of 50 feet per second after 1000 seconds

(c)

f(1000)−f(0)

1000−0

= 50 means

the plane's altitude increased an average of 50 feet per second over 1000 seconds

(d)

1

1000

1000	f(t)dt
0

is the plane's average altitude over 1000 seconds, in feet

(e)

d

dx

x	f(t)dt
0

is the plane's average altitude function

(f)

1000	f'(t)dt
0

= 50 means

the net change in the altitude of the plane over 1000 seconds is 50 feet