BC 1
Problem Set #5
Spring 2014
Name
Due Date: Monday 31 Mar. (at beginning of class)
Extra credit if turned in 10 day early
Please show appropriate work – no big calculator leaps – except as indicated. Work should be shown
clearly, using correct mathematical notation. 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.
Differentiate the following function. Don’t even think of simplifying or using the TI-89!
f ( x) 
2.
   sin 4 x3
 
 x2  2 x 
ln 3 x 2
Suppose
f x2  2 x
h  x 
, f (0)  4, f (4)  2, f (8)  3, f   0   3, f   2   3, f   4   5, f   6   7,
f ( x)
and f  8  2 . Determine the value of h  4  , if possible, showing your work.


BC 1
Problem Set #5
Spring 2014
3.
Suppose (1) = 0 and that  is the
function graphed at the right. If
Name
Due Date: Monday 31 Mar. (at beginning of class)
Extra credit if turned in 10 day early
Graph of 
G  x      x   , is G concave up
5
or concave down at x = –4?
Justify your answer.
4. Find all points (a, b) on the graph of f ( x)  2e x such that the tangent line to f at goes through the
point (1, 0) .
2
BC 1
Problem Set #5
Spring 2014
5.
Name
Due Date: Monday 31 Mar. (at beginning of class)
Extra credit if turned in 10 day early
Let h  x     g  x   . Use the graphs of f and g below to estimate the values of x where the graph of
h has stationary points. (That is, estimate all values of x such that h( x)  0 ).
y = f(x)
y = g(x)