Worksheet 2.9 - Derivatives Of Exponential Functions With Answers Page 6
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6Calculus Maximus
WS 2.9: Derivs of Exp Functs
+
<
⎧ ⎪
ax b x
,
0
( )
( )
= ⎨
+
_____ 21. Let
. If
f x is differentiable for all x, what is the value of a b
f x
x
>
⎪ ⎩
e
,
x
0
−
(A) 1
(B) 0
(C) 1
(D) 2
(E) 3
(
)
+
3 3
h
9
−
3
e
3
e
=
_____ 22.
lim
h
→
h
0
9
9
(A) 0
(B) 3
(C)
3e
(D)
9e
(E) nonexistent
t ≥
_____23. A unicorn moves along the x-axis so that its position at time t, in seconds,
is given by
0
2
t
⎛ ⎞
1
( )
2
= ⋅ ⎜ ⎟
t = second? Note:
x t
3
feet. In
ft/sec , what is the unicorn’s acceleration at
1
⎝ ⎠
2
(
)
2
2
=
ln
x
ln
x
.
⎛ ⎞
1
2
2
(A) 3
(B)
ln
(C) 12
(D) 3ln 2
(E)
3ln 2
⎜ ⎟
⎝ ⎠
2
Page 6 of 6
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