5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book April 11, 2018 15:14

More Applications of Derivatives 219

10.5 Practice Problems

Part A The use of a calculator is not

allowed.

1. Find the linear approximation of f(x)=
   (1+x)^1 /^4 atx=0 and use the equation to
   approximatef(0.1).


2. Find the approximate value of^3

√

28 using

linear approximation.

3. Find the approximate value of cos 46◦using
   linear approximation.


4. Find the point on the graph ofy=

∣∣

x^3

∣∣

such that the tangent at the point is parallel

to the liney− 12 x=3.

5. Write an equation of the normal line to the
   graph ofy=exatx=ln 2.


6. If the liney− 2 x=bis tangent to the graph
   y=−x^2 +4, find the value ofb.


7. If the position function of a par-
   ticle iss(t)=
   t^3
   3
   − 3 t^2 +4, find the velocity and
   position of the particle when its acceleration is 0.


8. The graph in Figure 10.5-1 represents the
   distance in feet covered by a moving particle
   intseconds. Draw a sketch of the
   corresponding velocity function.

5

4

3

2

1

0 12345

s(t)

t

Seconds

Feet

s

Figure 10.5-1

9. The position function of a moving particle
   is shown in Figure 10.5-2.

t 1 t 2

t 3

s(t)

s

t

Figure 10.5-2

For which value(s) oft(t 1 ,t 2 ,t 3 ) is:

(a) the particle moving to the left?

(b) the acceleration negative?

(c) the particle moving to the right and

slowing down?

10. The velocity function of a particle is shown
    in Figure 10.5-3.

(^01)
1

• 1


• 2


• 3


• 4


• 5

2

3

4

5

234

v(t)

v

t

Figure 10.5-3

(a) When does the particle reverse

direction?

(b) When is the acceleration 0?

(c) When is the speed the greatest?