MA157 Fall 2023
Quiz 1
1. ( 3 points) Suppose a function is defined by the following table:
X
f(x)
0 1 2 3 4 5
2 5 9 7 14 10
Calculate the average rate of change off on the interval [1, 4] .
.f (X4 ) - +(J< , )
=
~-x,
11 - S ~
4-,
~-r=@J
2. (3 points) Suppose the position (in meters) of an object is determined by the following
function (where t is in seconds):
p(t) = t 2 + 2t
Calculate the average rate of change of the position of the object on the interval, [O, 2], i.e.
from Oto 2. Include the units in your answer.
f (_xl+~) -f (X,) ,f{z.) -f(o") .: (t._1 +4-),-o .. B
-
~
\,-.
Z-
-
z
-r~ / /
--z--,f'\S
3. ( 6 points) For the following functions, write out and simplify the general difference quotient
f( x + h) - f(x)
h
(a) f (x) = 5x - 2
[5(x 1-\,, )-zJ
- (S~-z.)
i,
5/x + 5\,., - (: - ½x tL
-UL
~ .
~
(b) f (x) = x 2 + 1
1
( (x,. \,)
lx
r 1) -
),
C . "'
-i. 4-
.
t-\r.
yl -
I )
r ::
~
z,)\.\.i
+-~
\I)
\2]_
h1o
,
',..-/-o