BC 1
Problem Set #4
Spring 2014
Name
Due Date: Friday, March 7 (at beginning of class)
Please show appropriate work – no big calculator leaps – except as indicated. Work should be shown
clearly, using correct mathematical notation and written explanations as needed. Please show enough
work on all problems (unless specified otherwise) so that others could follow your work and do a
similar problem without help. Collaboration is encouraged, but in the end, the work should be your
own.
1.
If g(3) = –1 and –4 ≤ g(x) ≤ 5 for all x ≥ 0, find each of the following. Show work/thinking.
a.
the largest possible value for g(8)
b.
the smallest possible value for g(8)
c.
the largest possible value for g(0)
d.
the smallest possible value for g(0)
BC 1
Problem Set #4
Spring 2014
Name
Due Date: Friday, March 7 (at beginning of class)
2.
Sketch a graph of the function g(x) over the closed interval [–5, 5] given that g satisfies the
following conditions. Clearly identify all local maximum points, local minimum points, and inflection
points on your graph. Neatness and accuracy count.





g(–5) = 4 and g(5) = –6
g(x) > 0 only on the interval –2 < x < 1
g(x) < 0 only for –5 ≤ x < –2, 1 < x < 3, and 3 < x ≤ 5
g(x) > 0 only for –5 ≤ x < 0 and 2 < x < 3
g(x) < 0 only for 0 < x < 2 and 3 < x ≤ 5
BC 1
Problem Set #4
Spring 2014
3.
4.
Name
Due Date: Friday, March 7 (at beginning of class)
At the right is part of a table of values for a function h.
x
h(x)
4.0
1.8
4.2
1.1
4.4
0.7
4.6
0.4
a.
If h(x) is the derivative of a function k(x) (that is, k(x) = h(x)) and k(4) = –1, use Euler's
Method by hand to estimate k(4.6). Use three steps, showing work.
b.
Estimate the value of h(4.4). Show your calculation.
Each of the following limits represents the derivative of a function y  f ( x) at a particular value
of x, say x  a. For each limit, give the function f and the value of a. You do not need to evaluate
the limit.
 sin(  h)  sin( ) 
a. lim 

h 0
h

 e x  e4 
b. lim 

x2
 x  2 
f ( x)  ______________ and a  _______
2
 Ln( x ) 
c. lim 
x 1
 x  1 
f ( x)  ______________ and a  _______
f ( x)  ______________ and a  _______
 x  1  3x  3 
d. lim 

x 1
x 1


f ( x)  ______________ and a  _______
BC 1
Problem Set #4
Spring 2014
5.
Name
Due Date: Friday, March 7 (at beginning of class)
Is there a value c for which the function y  sin x  c, x  [0, 2 ] is tangent to y  ln x . If so, how
1
many different values? You may use the fact that the derivative of y  ln x is y  and the
x
derivative of y  sin x is y  cos x . Note: two functions f and g are tangent at x  a if and only if
f (a)  g (a) and f (a)  g (a) . Explain your answer clearly.