math
wenwen123
Lesson6-SlopeTangentVelocity-1.docxNAME: _______________________________________________________________________
1.
Find the equation of a tangent line that is tangent to the curve .
.
2.
Find the slope and then find the equation of a tangent line that is tangent to the curve.
.
3.
A. What is the slope of a tangent line to the function at a point?
.
B. What is the equation of the tangent line to that point?
4.
Assuming that a function represents the distance D measured in feet of a car that was slowing down respect to time t in seconds before it reached its destination.
a. What was the velocity of the car at 2 seconds? (Ans: V(3) = -15 ft/sec)
b. How many seconds did it take to make the car to come to a complete stop? (Ans: 3 sec)
c. What was the acceleration at 2 seconds? (Ans: A(2) = 12 ft/sec2)
5.
A ball is shot vertically up in the air from a hole on the ground with the initial velocity of 12 feet per second. The position of the ball in the air after t seconds is represented by the function where h: height of the ball in the air after t seconds and where t : time and, initial velocity and initial height respectively. Please find the following:
a.
How long would it take the ball to come back and hit the ground? ?
b.
What is the function velocity of the ball and what is the velocity of the moment of impact?
c.
What is the velocity of the ball after 2 seconds?
223
(:&:&)
Hintuseproductruleansmslopeyx
ppp
===-
(
)
tansin
x
yxx
=
2
42
(,)
p
32
2
(:)
ansmslope
==
32322
282
(:)
ansyx
p
=-+
(
)
3
27
t
Dxx
=-
2
00
()2
httvth
=-++
00
&:
vh
(:6sec)
anst
=
(:412&12/sec)
impact
ansVtVft
=-+=-
(:4/sec)
ansVft
=
(
)
23
(0,3)
51
x
x
fat
x
-
=
-
(:&:133)
Hintusequotientruleansyx
=+
(
)
2
tan(,0)
x
fxxat
p
=
