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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`

.