Worksheet #14
Math 221
Instructions. Put the first and last name of everyone in your workgroup at the top of your
paper. Everyone is to do their own worksheet but only one from each group is graded with
the score shared. Be sure to show your work and explain your reasoning.
1. Find the absolute maximum and minimum values for
f (x) = x3 − 9x2 + 24x − 15
on each of the following intervals (do not use a graphing device to solve these):
(a). [1, 3]
(b). [3, 5]
(c). [0, 6]
2. The Space Shuttle Challenger broke apart 73 seconds into its flight while traveling
approximately 18,000 miles per hour. Show that the shuttle experienced acceleration
of more than 320 feet per second squared at some point in its flight (that’s 10 times
earth’s gravity at sea level).
In[595]:=
Plot!"4!#x " 2$ " r%#2&, r%x&', "x, #2 , 4',
PlotStyle $ ""Red', "Blue, Thick'', PlotRange $ "0, r%4& " 2',
3. Suppose f (x) = Ax2 + Bx + C. Show that the
a " b number c that satisfies the conclusion
Ticks $ (("#2, "a"', (1, " a+b "), "4, "b"'), ""r%#2&, "f#a$"', "r%4&, "f#b$"'')*;
of the Mean Value Theorem is given by c = 22 .
In[596]:=
Show%%, %%, %%%, %%%%, %%%%%&
f!b"
f!a"
Out[596]=
a!b
a
In[597]:=
Out[597]=
2
b
2"2
4
4. Use the Mean Value Theorem to show that if f 0 (x) = 0 for all x ∈ (a, b) then f is a
constant function.
1