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# (Solved): Problems Given f(5)=10 and f^(')(5)=2, approximate f(6). Given P(100)=-67 and P^(')(100)=5, approxi ...

Problems Given

f(5)=10

and

f^(')(5)=2

, approximate

f(6)

. Given

P(100)=-67

and

P^(')(100)=5

, approximate

P(110)

. Given

z(25)=187

and

z^(')(25)=17

, approximate

z(20)

. Knowing

f(10)=25

and

f^(')(10)=5

and the methods de- scribed in this section, which approximation is likely to be most accurate:

f(10.1),f(11)

, or

f(20)

? Explain your rea- soning. Given

f(7)=26

and

f(8)=22

, approximate

f^(')(7)

. Given

H(0)=17

and

H(2)=29

, approximate

H^(')(2)

. Let

V(x)

measure the volume, in decibels, measured inside a restaurant with

x

customers. What are the units of

V^(')(x)

? Let

v(t)

measure the velocity, in

f(t)/(s)

, of a car moving in a straight line

t

seconds after starting. What are the units of

v^(')(t)

? The height

H

, in feet, of a river is recorded

t

hours after mid- night, April 1. What are the units of

H^(')(t)

?

P

is the profit, in thousands of dollars, of producing and sell- ing

c

cars. (a) What are the units of

P^(')(c)

? (b) What is likely true of

P(0)

?

T

is the temperature in degrees Fahrenheit,

h

hours after midnight on July 4 in Sidney, NE. (a) What are the units of

T^(')(h)

? (b) Is

T^(')(8)

likely greater than or less than 0 ? Why? (c) Is

T(8)

likely greater than or less than 0 ? Why? Review In Exercises 19-20, use the definition to compute the deriva- tives of the following functions.

f(x)=5x^(2)

f(x)=(x-2)^(3)

In Exercises 21 - 22, numerically approximate the value of

f^(')(x)

at the indicated

x

value.

f(x)=cosx

at

x=\pi

.

f(x)=\sqrt(x)

at

x=9

.

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