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MATH 30
PROBLEMS OF THE WEEK
SET 6
1.
A car speeding around a curve in the shape of
2
y
x
=
(moving from left to right)
skids off the road at the point
11
,
24
⎛
⎜
⎝⎠
⎞
⎟
.
Will the car hit a tree located at
3
1,
4
⎛⎞
⎜⎟
?
2.
To perform implicit differentiation on an equation such as
22
3
x
y
+=
x
1
we start by
differentiating all terms with respect to x.
We get
2
xy
x y
′
+
=
.
Many students
learn the rules this way:
Take “regular” derivatives of all terms, and tack on a
y
′
,
that is
dy
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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, Implicit Differentiation

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