Exploring Behaviors of Implicit Relations
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
What is a point of inflection for an implicit relation?
QUESTION
Find
d
y
d
x
\frac{dy}{dx}
d
x
d
y
for
x
2
+
x
y
+
y
2
=
7
x^2 + xy + y^2 = 7
x
2
+
x
y
+
y
2
=
7
implicitly.
QUESTION
Find
d
y
d
x
\frac{dy}{dx}
d
x
d
y
for
x
y
=
1
xy = 1
x
y
=
1
implicitly.
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ANSWER
d
y
d
x
=
−
y
x
\frac{dy}{dx} = -\frac{y}{x}
d
x
d
y
=
−
x
y
. Use product rule: derivative of
x
y
xy
x
y
when product equals constant.
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