60. Find the maximum volume of 3 Q2): that can be made by cutting squares from the corners of an
8 inch by 15 inch rectangu var sheet of cardboard and folding up the sides.
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10. f(x) =x2 ~4x on the intervauo, 4
12. f(x) =f3-1x219n the interval [3, 7]
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pm-lieie moves along the x axis such that its position, for t >
Use this W a: complete exercises 30 33.
30. Whatare evalues of p(2) and p"(2)?>lxplain what each value represents.
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6. For t it 0, the temperature of a cup of coffee in degrees Fahrenheit t minutes after it is poured is
modeled by the function F(t) = 68+ 93(091). Find the value of F (4). Using correct units of
measure, explain what this value rneans in the context of t
Fwe functions in cxcrises 22 and 23, determine if the Mean Value Theorem holds tmc for 0 < c < 5?
Give a reason for your answer. If it does hold true, nd the guaranteed value(s) of c. [CALC]
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35. If the position Ufa particle is dened by the function x0) = :3 -9:2 + 24: for r > o, is the speed of the
v particle increasing or decreasing when t = 2.5? Justify your answer.
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For exercises 15 18, determine whether the Mean Value Theoxem can be applied to the mction on the
indicated interval. If the Mean Value Theorem can e apphea: 33nd all values of c that satisfy the
15. f(x)= x3 -x 22;: on[-l, 1] 17. f(x)=~/x3 C
For exercises 55 ~ 62, solve the given optimization problem. Show your work and remember to justify
your answers. _ - IQ: , 8 a
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55. Find the point on the graph of f (x) = J x + 8 so that the point (2, 0) is closest to the graph. )
Using the graph of the mction,j(x), pictured above, and given the intervals in the table below, determine
if Rollcs or Mean Value Theorem, whichever is indicated, can be applied or not. Give reasons for your
answers. F ()9
in.m.T.r.-.r , .4.5.,.?.2.r.+.~.
Jeff leaves his house riding his bicycle toward school. His velocity v(t), measured in feet per minute, on
the interval 0 5 t 5 15, for t minutes, is shown in the graph to the right. Use the graph to complete
. exercises 51 - 54.
The graph below represents the position, p(t), of a particle that is moving along the x axis. Use the
graph to complete exercises 43 47. MID-SW and t is measured in seconds.
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43. For What interval(s) of time is the particle moving to th@ Justif
39. On what interva1(s) is the particle moving to th@? @ Justify your ayswet.
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40. On what interyaKs) is the parti cjfgwing dow
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A particle moves along the x - axis so that at any time 0 _<_ t g 5, the velocity, in meters per second, is
given by the function v(t) = (t - 2) cos 2! . Use a graphing calculator to complete exercises 48 - 50.
48 On the interval 0 st _<_ 5, at how many
U m f 'mBMKmws of the Derivative - Part II
1. For which of the following mctions is the Extreme Value Theorem NOT APPLICABLE on the
interval [a, 17]? Give a reason for your answer.
Graph 1 Graph II Graph III
58. A rectangle is bound by the x - axis and the graph of a semicircle dened by y :2 J25 -x2 . What
n length and width should the rectangle have so that its area is a maximum?
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