2.1 - Tangent Line Problem Worksheet With Answers - Calculus Maximus Page 6
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7Calculus Maximus
WS 2.1: Tangent Line Problem
( )
=
2
+
+
11. Using your calculator to zooooooom in, determine if
is locally linear at
h x
x
0.0001 0.99
x = . Give a reason for your answer.
0
Multiple Choice
_____ 12. A function will fail to be differentiable at all of the following except
(A) A vertical asymptote
(B) A removable discontinuity
(C) A cusp
(D) A vertical tangent line
(E) A horizontal tangent line
⎧
2
−
x
4
⎪
≠
,
x
2
( )
= ⎨ −
f x
x
2
⎪
=
1,
x
2
⎩
_____ 13. Let f be the function defined above. Which of the following statements about f are true?
( )
I.
lim
f x
exists
→
x
2
x =
II. f is continuous at
2
x =
III. f is differentiable at
2
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
( )
( )
( )
f ′
= and
= . Let
_____ 14. Let f be a differentiable function such that
f
2
1
2
4
T x be the equation
( )
( )
x = . What is the value of
of the tangent line to
f x at
2
T
1.9
?
(A) 0.4
(B) 0.6
(C) 0.7
(D) 1.3
(E) 1.4
Page 6 of 7
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