AP Calculus AB Quiz
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DIFFERENTIATION: DEFINITION AND FUNDAMENTAL PROPERTIES
Question 1
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The graph of
f
f
f
has a corner at
x
=
3
x=3
x
=
3
; which statement must be true about
f
′
(
3
)
f'(3)
f
′
(
3
)
?
A
It exists because
f
f
f
is continuous at
x
=
3
x=3
x
=
3
.
B
It does not exist because the one-sided derivatives are not equal at
x
=
3
x=3
x
=
3
.
C
It equals
0
0
0
because corners occur at local extrema.
D
It exists but is infinite because corners imply vertical tangents.
E
It does not exist because
f
f
f
must be discontinuous at
x
=
3
x=3
x
=
3
.
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