Spring 2026 Written Assignment 2
MA 113: Calculus I
Written Assignment 2 (Due on 02/04/26 at 11:59 pm)
NAME:
Instructions: The purpose of this assignment is to develop your ability to formulate
and communicate mathematical arguments. Unreadable work may receive no credit.
You should provide well-written, complete answers to each of the questions. We will
look for correct mathematical arguments, complete explanations, and correct use of English.
Your solution should be formulated in complete sentences. As appropriate, you may want to
include diagrams or equations written out on a separate line. You may read your textbook
to find examples of how we communicate mathematics. You should also read the page about
writing mathematics in the general information section of our Canvas shell.
Students may use word processing software, a writing app on a tablet or pencil and paper
to prepare their solutions. It may be simpler to draw graphs and mathematical expressions
by hand. The final solution must be prepared as a single pdf and uploaded to Canvas. For
those that write their solutions on paper, a tablet or phone can be used to produce a pdf
of their work. Scanning functionality is built into Google Drive and the Files app on Apple
products. Since you are submitting this paper in Canvas, there is no need to put your name
on your work. We suggest that you not include your name as we may use the option within
Canvas to grade anonymously.
1. Consider the function f(x) = 2
√
x.
(a) For a > 0, form the difference quotient
f(a + h) − f(a)
h
and simplify this difference quotient to obtain an expression which may be eval-
uated at h = 0.
(b) Use the definition of the derivative (see Definition 2.2.1 in CLPI) to find f→(a)
for a > 0,
f
→(a) = lim
h→0
f(a + h) − f(a)
h
(c) Find the tangent line to the graph of f at x = 9.
(d) Find the inverse function f−1 and give the domain and range of f−1
.
(e) Use the definition of the the derivative to find the derivative of f−1 at 6. (Note
that f(9) = 6.)
(f) How are the derivatives f→(9) and (f−1)→(6) related?
1
Vinnte
Inglam
f(a)
=
2va
感
2
会
22
ia
π
(
2
ππµ
)
?
-
cara
"
,
nva
,
Flath) =
+
=
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+
h)
-
4a
sra
.
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-
"
ats
'
n
-
Ya
tarainaara
√
()
.
x
+
9f'(a)
⑤
revostaraia
'
ra
(
afeava
)
落号
Subin
>
h
=
@
f(ap
=
2rq
=
2(3)
=
6
→
最⼼
m
然
⑤σ
癌话它
tangency
.
s(a
,
6)
2
-
y
,
=
m(X
-
x
,
)
は
6
×
る
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ipciprocals
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oth of
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(f
")'17
ital
invese
function
is
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10)
any
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ay
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6
]
:
}
9
N
Theotem-
is
[0
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)
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^
"
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6
+
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]
;
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]
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—
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”
。
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36
x
1
☆
算
。
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=
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6
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n
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d
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