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2.1 - #1

What is the slope of the line tangent to the graph of f at (a,f(a))?

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2.1 - #2

The position of an object moving along a line is given by the fnction s(t) ! -".2$

%%t $ 2%. &in' the average velocity of the object over the folloing intervals.

(a) *, %+

(b) *, 2+(c) *, 1+(') *, 1 $ h+, here h -1 is any real nmber

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2.1 - #2 ample

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2.1 - #%

The table gives the position s(t) of an object moving along a line at time t, over a

to-secon' interval. &in' the average velocity of the object over the folloing

intervals.

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2.1 - #% ample

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2.1 - #"

/onsi'er the position fnction s(t) ! sin(0t) representing the position of an object

moving along a line on the en' of a spring. etch a graph of s ith the secant line

passing throgh (*, s(*)) an' (*.", s(*.")). 3etermine the slope of the secant line

an' eplain its relationship to the moving object.

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2.1 - #4

&or the position fnction s(t)!225t$1, complete the folloing table ith the

appropriate average velocities. Then mae a conjectre abot the vale of the

instantaneos velocity at t!*.

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2.1 - #4 ample

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2.1 - #6

a. 7raph the fnction f()!28 12 $ %4.

b. 9'entify the point (a, f(a)) at hich the fnction has a tangent line ith :ero slope.

c. /on;rm yor anser to part (b) by maing a table of slopes of secant lines to

approimate the slope of the tangent line at this point.

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2.1 - #6 ample

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2.1 - # the e'ge of a cli> an' its 'istance s (in feet) from the top of

the cli> after t secon's is s(t) ! 16t2. =ssme the 'istance from the top of the cli> to

the ater belo is 126 ft. =nser part (a) an' (b).

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2.1 - #< ample

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