Free Response
Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or
other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under
which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of
your methods as well as your answers. Answers without supporting work will usually not receive credit.
14. Let h be a function defined for all x 0 such that h(4)=-3 and the derivative of his given by
h'(x)=
for all x 0.
x
(a) Find all the values of x for which the graph of h has a horizontal tangent line.
X=1
15.
(b) Write an equation for the line tangent to the graph of h at x = 4.
16. Letfbe the function defined by
X
f(z) =
2
√z+1 for 0 <=<3
5-z
for 3 < x < 5.
I
3
4
5
(a) Is f continuous x=3? Explain why or why not.
-2
8
Let f be a function that is differentiable for all real numbers. The table above gives values for fat selected
points in the closed interval 2≤x≤13. Estimate f'(4).
3
13
6
(b) Find the average rate of change of f(x) on the closed interval of 0≤x≤5.