Download jan 31

name:
Mathematics 141 sixth homework
due Friday, January 31, 2014
show your work to get credit for each problem
21. Simplify the difference quotient
f (x + h) − f (x)
for the function f (x) = x2 −4x .
h
22. Solve the equation f (x) = g(x) if f (x) = x2 − 4x and g(x) is the linear function for
which g(1) = −1 and g(3) = 1.
23. For the quadratic function F (x) = x2 − 9x − 4
(a) solve F (x) = 0 by the completing the square method
(b) rewrite F (x) in the format F (x) = (x − a)2 + b
(c) rewrite F (x) in the factored format F (x) = (x − x1 )(x − x2 ), where x1 and x2 are real
number constants.
(d) calculate the average rate of change in the values of F from x = 0 to x = 1/1000.
24. For the quadratic function
f (x) = 2 − 8x + .001x2
(a) graph the function. Be sure to label the exact coordinates of the parabola’s vertex and
x and y intercepts.
(b) what is the range of the function f ?
(c) for which values of x is the function f increasing ?
(d) solve the equation f (x) > 0
25. (a continuation of problem (16))
Suppose that a city’s transit ridership x and the price per ride p are linearly related. The
transit ridership is two million when the fare is $2 per ride, while the ridership is only 1.75
million when the fare is $2.10.
(a) find the linear relation between x and p
(b) the total revenue from fares R = px. Write R as a function of p.
(c) calculate the price p which maximizes revenue R.
(d) what is the maximum revenue possible?
page two
26. An object is thrown upwards from the ground with an initial velocity of 30 meters per
second. Its height (in meters) as a function of time t in seconds is given by
H(t) = 30t − 4.9t2 (on the earth)
h(t) = 30t − 0.8t2 (on the moon)
(a) calculate the maximum height of the object above the earth and the time it attains the
maximum height
(b) calculate the time on earth at which the object hits the ground.
(c) calculate the maximum height of the object above the moon and the time it attains
the maximum height
(d) calculate the time on moon at which the object hits the ground.