an application of the fundamental theorem of calculus: rate graphs
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An Application of the fundamental theorem of calculus: Rate graphs. Section 4-L. The graph of a function f consists of a quarter circle and line segments. Let g be the function given by. a) Find. Graph of f. Find all values of x on the open interval - PowerPoint PPT PresentationTRANSCRIPT
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AN APPLICATION OF THE FUNDAMENTAL THEOREM OF CALCULUS: RATE GRAPHS
Section 4-L
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0
xg x f t dt
0 , 1 , 2 , 5g g g g
1) The graph of a function f consists of aquarter circle and line segments. Let g be the function given by
.
Graph of f
a) Find
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.
1, 5
1, 5
Graph of f
b) Find all values of x on the open intervalat which g has a relative maximum
c) Find the absolute minimum value of g on
And the value of x at which it occurs
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. 1, 5
Graph of f
d) Find the x-coordinate of each point of inflection of the graph of g on
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2) x
dtt
t
dx
d
3
sin
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3) The graph of the velocity , in ft/sec, of a car travelingon a straight road, for is shown in the figure.
a) Find the average acceleration of the car, over the interval
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b) Find an approximation for the acceleration of the car at t = 20.
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c) Approximate with a Riemann sum, using the midpoints of three subintervals of equal length. Explain the meaning of this integral.
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4) (modification of 2006 BC 4)Rocket A has positive velocity v(t) after being launched upward from an initial height of 0 feet at time t = 0 seconds. The velocity of the rocket is recorded for selected values of t over the interval seconds as shown in the table below
t (seconds) 0 10 20 30 40 50 60 70 80
(ft per sec) 5 14 22 29 35 40 44 47 49
800 t
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4) (modification of 2006 BC)a) Explain the meaning of in terms of the rocket’s flight. Use a midpoint Riemann sum with 3 subintervals of equal length to approximate
70
10v t dt
70
10v t dt
t (seconds) 0 10 20 30 40 50 60 70 80
(ft per sec) 5 14 22 29 35 40 44 47 49
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4) (modification of 2006 BC)b) Rocket B is launched upward with an acceleration
of
feet per second per second. At time t=0 seconds, the initial height of the rocket is 0 feet, and the initial velocity is 2 feet per second. Which of the two rockets is traveling faster at t = 80 seconds?
3
1a t
t
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HOME WORKWorksheet 4-L and FRQ 4