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MATH 30
PROBLEMS OF THE WEEK
SET 4
These problems are due on October 8.
1.
Given
( )
2
3
f x
x
x
, find all values of
x
where the function is not
differentiable.
Justify your answer in terms of the definition of the derivative.
That is,
0
(
)
( )
lim
h
f x h
f x
fx
h
.
When would this limit fail to exist?
2.
Sometimes an incorrect method accidentally produces a correct answer.
For
quadratic functions (but
definitely not most
other functions, the average velocity
between time
ta
and time
tb
equals the average of the velocities at
and
.
To show this, assume
2
()
f t
At
Bt C
is the position function.
Show that the average velocity between
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This note was uploaded on 01/07/2010 for the course MATH 1 taught by Professor Staff during the Spring '08 term at UC Davis.
 Spring '08
 Staff
 Math, Derivative

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