(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)=10and
f^(')(5)=2, approximate
f(6). Given
P(100)=-67and
P^(')(100)=5, approximate
P(110). Given
z(25)=187and
z^(')(25)=17, approximate
z(20). Knowing
f(10)=25and
f^(')(10)=5and 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)=26and
f(8)=22, approximate
f^(')(7). Given
H(0)=17and
H(2)=29, approximate
H^(')(2). Let
V(x)measure the volume, in decibels, measured inside a restaurant with
xcustomers. 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
tseconds after starting. What are the units of
v^(')(t)? The height
H, in feet, of a river is recorded
thours after mid- night, April 1. What are the units of
H^(')(t)?
Pis the profit, in thousands of dollars, of producing and sell- ing
ccars. (a) What are the units of
P^(')(c)? (b) What is likely true of
P(0)?
Tis the temperature in degrees Fahrenheit,
hhours 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
xvalue.
f(x)=cosxat
x=\pi .
f(x)=\sqrt(x)at
x=9.
