Graphs of Functions: Properties of Functions575Problems 69-76, use a graphing utility to graph each function over the indicated interval andHithere it is decreasing. Round answers to two decimal places.pproximate any local maxima and local minima. Determine where the function is increasing andn Ja)=*- 3x + 2; (-2, 2)71.fax) = x-x'; (-2, 2)73. Rx) = I0.2x- 0.6x2 4x - 6; (-6,4)71 Ja3)= 0.25x4 + 0.3x3-0.9x2 +3; (-3, 2)17. For the function f(x) = x, compute each average rate of70. f(x) = x - 3x2 +5; (-1,3)72. f(x) = x-(-2,2)74. f(x) = 0.4x3 + 0.6x2+ 3x- 2; (-4,5)76. f(x) =0.4x4- 0.5x + 0.8x2-2; (-3,2)(2,2)(a) Determine the height of the golf ball after it has traveled100 feet.(b) What is the height after it has traveled 300 feet?(c) What is the height after it has traveled 500 feet?(d) How far was the golf ball hit?(e) Use a graphing utility to graph the function h = h(x).(f) Use a graphing utility to determine the distance that theball has traveled when the height of the ball is 90 feet.(g) Create a TABLE with TblStart = 0 and ATbl 25.(h) To the nearest 25 feet, how far does the ball travel before itreaches a maximum height? What is the maximum height?(i) Adjust the value of ATbl until you determine the dis-tance, to within 1 foot, that the ball travels before itreaches a maximum height.change:(a) from 0 to 1(c) from 0 to 0.1(e) from 0 to 0.001from 0 to 0.5(b)from 0 to 0.01(d)(3,0)X()Graph each of the secant lines. Set the viewing rectangleto: Xmin=0.2, Xmax1.2, Yscl1.2, Xscl = 0.1, Ymin =-0.2,0.1.YmaxQ (8)What do you think is happening to the secant lines?Q(h) What is happening to the slopes of the secant lines?Is there some number they are getting closer to? What isthat number?78. For the function f(x)= x, compute each average rate ofchange:80. Effect of Elevation on Weight If an object weighs mpounds at sea level, then its weight W (in pounds) at a heightof h miles above sea level is given approximately by(a) from 1 to 2(c) from 1 to 1.1(e) from 1 to 1.001(f) Graph each of the secant lines. Set the viewing rectangle(b) from 1 to 1.5(d) from 1 to 1.0124000W (h)т4000 h2.5, Xsclto: XminYmax = 4, Yscl = 0.1.0.1, Ymin- 0.5, Xmax-1,(a) If Amy weighs 120 pounds at sea level, how much willshe weigh on Pike's Peak, which is 14,110 feet above sealevel? (1 mile =5280 feet)(b) Use a graphing utility to graph the function W W (h).Use m(c) Create a Table with TblStart 0 and ATbl= 0.5 to seehow the weight W varies as h changes from 0 to 5 miles.(d) At what height will Amy weigh 119.95 pounds?Q(e) Does your answer to part (d) seem reasonable?Qe ()What do you think is happening to the secant lines?Qih) What is happening to the slopes of the secant lines? Isthere some number they arethat number?getting closer to? What is120 pounds.11179. Motion of a Golf Ball A golf ball is hit with an initial veloci-of 130 feet per second at an inclination of 45° to the hori-tyzontal. In physics, it is established that the height h of thegolf ball is given by the function81. Constructing an Open Box An open box with a square baseis to be made from a square piece of cardboard 24 inches ona side by cutting out a square from each corner and turningup the sides (see the figure).-32x21302+xh(x)where x is the horizontal distance that the golf ball has traveled.хX24 in.xX24 in.

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I don’t know how to do number 74 on this page, and the steps 

Graphs of Functions: Properties of Functions
575
Problems 69-76, use a graphing utility to graph each function over the indicated interval and
Hithere it is decreasing. Round answers to two decimal places.
pproximate any local maxima and local minima. Determine where the function is increasing and
n Ja)=*- 3x + 2; (-2, 2)
71.fax) = x-x'; (-2, 2)
73. Rx) = I0.2x- 0.6x2 4x - 6; (-6,4)
71 Ja3)= 0.25x4 + 0.3x3-0.9x2 +3; (-3, 2)
17. For the function f(x) = x, compute each average rate of
70. f(x) = x - 3x2 +5; (-1,3)
72. f(x) = x-(-2,2)
74. f(x) = 0.4x3 + 0.6x2+ 3x- 2; (-4,5)
76. f(x) =0.4x4- 0.5x + 0.8x2-2; (-3,2)
(2,2)
(a) Determine the height of the golf ball after it has traveled
100 feet.
(b) What is the height after it has traveled 300 feet?
(c) What is the height after it has traveled 500 feet?
(d) How far was the golf ball hit?
(e) Use a graphing utility to graph the function h = h(x).
(f) Use a graphing utility to determine the distance that the
ball has traveled when the height of the ball is 90 feet.
(g) Create a TABLE with TblStart = 0 and ATbl 25.
(h) To the nearest 25 feet, how far does the ball travel before it
reaches a maximum height? What is the maximum height?
(i) Adjust the value of ATbl until you determine the dis-
tance, to within 1 foot, that the ball travels before it
reaches a maximum height.
change:
(a) from 0 to 1
(c) from 0 to 0.1
(e) from 0 to 0.001
from 0 to 0.5
(b)
from 0 to 0.01
(d)
(3,0)
X
()Graph each of the secant lines. Set the viewing rectangle
to: Xmin=0.2, Xmax
1.2, Yscl
1.2, Xscl = 0.1, Ymin =-0.2,
0.1.
Ymax
Q (8)What do you think is happening to the secant lines?
Q(h) What is happening to the slopes of the secant lines?
Is there some number they are getting closer to? What is
that number?
78. For the function f(x)= x, compute each average rate of
change:
80. Effect of Elevation on Weight If an object weighs m
pounds at sea level, then its weight W (in pounds) at a height
of h miles above sea level is given approximately by
(a) from 1 to 2
(c) from 1 to 1.1
(e) from 1 to 1.001
(f) Graph each of the secant lines. Set the viewing rectangle
(b) from 1 to 1.5
(d) from 1 to 1.01
2
4000
W (h)
т
4000 h
2.5, Xscl
to: Xmin
Ymax = 4, Yscl = 0.1.
0.1, Ymin
- 0.5, Xmax
-1,
(a) If Amy weighs 120 pounds at sea level, how much will
she weigh on Pike's Peak, which is 14,110 feet above sea
level? (1 mile =5280 feet)
(b) Use a graphing utility to graph the function W W (h).
Use m
(c) Create a Table with TblStart 0 and ATbl= 0.5 to see
how the weight W varies as h changes from 0 to 5 miles.
(d) At what height will Amy weigh 119.95 pounds?
Q(e) Does your answer to part (d) seem reasonable?
Qe ()What do you think is happening to the secant lines?
Qih) What is happening to the slopes of the secant lines? Is
there some number they are
that number?
getting closer to? What is
120 pounds.
1
11
79. Motion of a Golf Ball A golf ball is hit with an initial veloci-
of 130 feet per second at an inclination of 45° to the hori-
ty
zontal. In physics, it is established that the height h of the
golf ball is given by the function
81. Constructing an Open Box An open box with a square base
is to be made from a square piece of cardboard 24 inches on
a side by cutting out a square from each corner and turning
up the sides (see the figure).
-32x2
1302
+x
h(x)
where x is the horizontal distance that the golf ball has traveled.
х
X
24 in.
x
X
24 in.
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Graphs of Functions: Properties of Functions 575 Problems 69-76, use a graphing utility to graph each function over the indicated interval and Hithere it is decreasing. Round answers to two decimal places. pproximate any local maxima and local minima. Determine where the function is increasing and n Ja)=*- 3x + 2; (-2, 2) 71.fax) = x-x'; (-2, 2) 73. Rx) = I0.2x- 0.6x2 4x - 6; (-6,4) 71 Ja3)= 0.25x4 + 0.3x3-0.9x2 +3; (-3, 2) 17. For the function f(x) = x, compute each average rate of 70. f(x) = x - 3x2 +5; (-1,3) 72. f(x) = x-(-2,2) 74. f(x) = 0.4x3 + 0.6x2+ 3x- 2; (-4,5) 76. f(x) =0.4x4- 0.5x + 0.8x2-2; (-3,2) (2,2) (a) Determine the height of the golf ball after it has traveled 100 feet. (b) What is the height after it has traveled 300 feet? (c) What is the height after it has traveled 500 feet? (d) How far was the golf ball hit? (e) Use a graphing utility to graph the function h = h(x). (f) Use a graphing utility to determine the distance that the ball has traveled when the height of the ball is 90 feet. (g) Create a TABLE with TblStart = 0 and ATbl 25. (h) To the nearest 25 feet, how far does the ball travel before it reaches a maximum height? What is the maximum height? (i) Adjust the value of ATbl until you determine the dis- tance, to within 1 foot, that the ball travels before it reaches a maximum height. change: (a) from 0 to 1 (c) from 0 to 0.1 (e) from 0 to 0.001 from 0 to 0.5 (b) from 0 to 0.01 (d) (3,0) X ()Graph each of the secant lines. Set the viewing rectangle to: Xmin=0.2, Xmax 1.2, Yscl 1.2, Xscl = 0.1, Ymin =-0.2, 0.1. Ymax Q (8)What do you think is happening to the secant lines? Q(h) What is happening to the slopes of the secant lines? Is there some number they are getting closer to? What is that number? 78. For the function f(x)= x, compute each average rate of change: 80. Effect of Elevation on Weight If an object weighs m pounds at sea level, then its weight W (in pounds) at a height of h miles above sea level is given approximately by (a) from 1 to 2 (c) from 1 to 1.1 (e) from 1 to 1.001 (f) Graph each of the secant lines. Set the viewing rectangle (b) from 1 to 1.5 (d) from 1 to 1.01 2 4000 W (h) т 4000 h 2.5, Xscl to: Xmin Ymax = 4, Yscl = 0.1. 0.1, Ymin - 0.5, Xmax -1, (a) If Amy weighs 120 pounds at sea level, how much will she weigh on Pike's Peak, which is 14,110 feet above sea level? (1 mile =5280 feet) (b) Use a graphing utility to graph the function W W (h). Use m (c) Create a Table with TblStart 0 and ATbl= 0.5 to see how the weight W varies as h changes from 0 to 5 miles. (d) At what height will Amy weigh 119.95 pounds? Q(e) Does your answer to part (d) seem reasonable? Qe ()What do you think is happening to the secant lines? Qih) What is happening to the slopes of the secant lines? Is there some number they are that number? getting closer to? What is 120 pounds. 1 11 79. Motion of a Golf Ball A golf ball is hit with an initial veloci- of 130 feet per second at an inclination of 45° to the hori- ty zontal. In physics, it is established that the height h of the golf ball is given by the function 81. Constructing an Open Box An open box with a square base is to be made from a square piece of cardboard 24 inches on a side by cutting out a square from each corner and turning up the sides (see the figure). -32x2 1302 +x h(x) where x is the horizontal distance that the golf ball has traveled. х X 24 in. x X 24 in.

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Expert Answer

Step 1

Given:

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f (x)-0.4x5 0.6x2 +3x - 2 [4,5

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Step 2

Differentiate the function with respect to ‘x’ and simply the derivative:

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d (x) dx d x 0.6 d x 3 dx f(x)0.4 (2) f'(x)-0.4x3.x* +0.6x2x +3-0 f'(x)1.22 +1.2x +3 12x2 12x +3 10 12 :1.2 = 10 f'(x)= + 10 6x2 6x 3 f(x) 5 5 1 f(r 6x+6x +15 5

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Step 3

Find the critical points by pu...

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6x26x15 0 + f'(x)= -6x26x15 = 0 -3(2x2-2x-5)0 -3] taking common 2x2-2x-5 0

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