Connecting Differentiability and Continuity
AP Calculus AB · Flashcards · Application
AP CALCULUS AB · FLASHCARDS
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QUESTION
Determine the differentiability of
f
(
x
)
=
x
2
+
3
x
+
2
f(x) = x^2 + 3x + 2
f
(
x
)
=
x
2
+
3
x
+
2
at
x
=
−
1
x = -1
x
=
−
1
.
QUESTION
Determine the differentiability of
f
(
x
)
=
floor
(
x
)
f(x) = \text{floor}(x)
f
(
x
)
=
floor
(
x
)
at
x
=
2
x = 2
x
=
2
.
QUESTION
For
f
(
x
)
=
1
x
f(x) = \frac{1}{x}
f
(
x
)
=
x
1
, is
f
(
x
)
f(x)
f
(
x
)
differentiable at
x
=
0
x = 0
x
=
0
?
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ANSWER
No,
f
(
x
)
f(x)
f
(
x
)
is undefined at
x
=
0
x = 0
x
=
0
. Function is undefined at
x
=
0
x = 0
x
=
0
.
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