Math1210 Weekly Assignment 5
(Derivatives, Chain Rule, Higher order
Derivatives 2.4-2.6)
Spring, 2016
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 equation of the tangent line to the graph of the following
functions at the point x = π
(a) (5 points) f (x) = tan x
Answer:
(b) (5 points) f (x) = sin3 (2x)
Answer:
(c) (5 points) f (t) = sin x cos x
Answer:
(d) (5 points)
sin 2x
2 cos2 x
Answer:
2. (10 points) Let f (π) = π and f 0 (π) =
x=π
√
4
7. Find the derivative of f (f (f (f (x)))) at
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3. (20 points) Sketch the graph of a function that satisfies all of the given conditions.
(a)
i. f 0 (x) < 0
ii. f 00 (x) < 0 for all x
(b)
i. f 00 (x) < 0 for 0 < x < 2
iii. f 0 (0) = f 0 (3) = 0
iv. f 0 (x) < 0 for x < 0 and 0 < x < 3
v. f 0 (x) > 0 for x > 3
ii. f 00 (x) > 0 for −∞ < x < 0 and
2<x<∞
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4. (15 points) In the following graphs, determine which curves are the original function,
and which are it’s first and second derivative.
(a)
original function:
red
green
blue
first derivative:
red
green
blue
second derivative:
red
green
blue
(b)
original function:
red
green
blue
first derivative:
red
green
blue
second derivative:
red
green
blue
(c)
original function:
red
green
blue
first derivative:
red
green
blue
second derivative:
red
green
blue
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