Math1210 Weekly Assignment 4
Spring, 2016
(Derivatives 2.1-2.3)
instructor:
Uid number:
name:
Instructions: Please show all of your work as partial credit will be given where appropriate,
and there may be no credit given for problems where there is no work shown. All answers
should be completely simplified, unless otherwise stated. No calculators or electronics of
any kind are allowed. (Total of 65 points possible.)
1. (20 points) Find the slope of the tangent line to the graph of the following functions at
the point x = 1
(a) (5 points) f (x) = 3x2 − 4x + 1
Answer:
(b) (5 points) f (x) = x
−2
Answer:
(c) (5 points) f (t) =
1
t+3
Answer:
√
(d) (5 points) f (x) = ( 2 − x)(x2 − 3x + 1)
Answer:
2. (20 points) The given limit is a derivative, but of what function and at what point?
[You don’t have to evaluate the limit]
√
4
(a) (5 points) lim
h→0
16 + h − 2
h
Answer:
5
x − 32
x→2 x − 2
(b) (5 points) lim
Answer:
cos(π + h) + 1
h→0
h
(c) (5 points) lim
Answer:
4
t +t−2
t→1
t−1
(d) (5 points) lim
Answer:
Page 2
3. (15 points) The graph of f is given. Find the numbers at which f is not differentiable
and state why (corner, discontinuity or vertical tangent). [Hint: See Figure 4 on page
103 of the text]
(a) (5 points)
Answer:
(b) (5 points)
Answer:
(c) (5 points)
Answer:
Page 3
1
4. (10 points) Find all points on the graph of y = x3 − 16x + 2 where the tangent line is
3
horizontal.
Page 4