MAT 137Y: Calculus!
Problem Set A.
This problem set is intended to help you prepare for Test #1. It is not compre
hensive: it only contains problems from some sections that were not included in past
problem sets or in past tutorials. You do not need to turn in any of these problems.
1. Compute the derivative of the following functions:
•
f
(
x
) =
x
9

9
x
3
+ 2
x
•
f
(
x
) =
x
2
+ 2
x
x
3

x
•
f
(
x
) =
1 +
x
3
x
•
f
(
x
) =
√
x
(
x
+ 7
3
√
x
)
2. In each of the following four grids we sketch the graph of a function. Sketch the graphs of
their derivatives.
(a)
1
2
3
4
1
2
3
4
1
2
3
1
2
3
(b)
1
2
3
4
5
6
1
2
3
4
5
1
2
3
4
1
2
3
y=f(x)
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1
2
3
4
1
2
3
4
1
2
3
1
2
3
(d)
1
2
3
4
5
6
1
2
3
4
5
1
2
3
4
1
2
3
y=f(x)
3. Consider the function
f
(
x
) =
1
√
x
+ 2
. Use the deﬁnition of derivative as a limit to compute
f
0
(

1).
4. Consider the function
g
(
x
) =
(
x
3

5
if
x
≥
2
ax
+
b
if
x <
2
where
a
and
b
are constants. What are the values of
a
and
b
that will make
g
diﬀerentiable
everywhere?
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 Fall '08
 UPPAL
 Calculus, Derivative, Sets, Continuous function, 1, 3, 2

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