Ma 113 Functions And Inverse Functions, The Exponential Function And The Logarithm Worksheet Page 41
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4121. A rectangular storage container with an open top is to have a volume of 10 cubic meters. The length of
the container is twice its width. Material for the base costs $10 per square meter while material for the
sides costs $6 per square meter. Find the cost of materials for the least expensive possible container.
22. (a) State the Mean Value Theorem.
(b) If 3
f (x)
5 for all x, find the maximum possible value for f (8)
f (2).
11π
23. Use linearization to approximate cos(
)
60
(a) Write down L(x) at an appropriate point x = a for a suitable function f (x).
11π
(b) Use part(a) to find an approximation for cos(
)
60
(c) Find the absolute error in your approximation.
24. Find the value(s) c such that f (x) is continuous everywhere.
3
(cx)
if x < 2
f (x) =
c
ln(x
) if x
2
3
3
25. (a) Find y if x
+ y
= 6xy.
(b) Find the equation of the tangent line at (3, 3).
5
3
26. Show that the function f (x) = 3x
20x
+ 60x has no absolute maximum or minimum.
27. Compute the following definite integrals:
1
9
x
1
u+1
(a)
e
du
(c)
dx
x
1
1
2
10
2
(b)
4
x
dx
(d)
x
5 dx
2
0
Hint: For some of the integrals, you will need to interpret the integral as an area and use facts from
geometry to compute the integral.
b
28. Write as a single integral in the form
f (x) dx:
a
2
5
1
f (x) dx +
f (x) dx
f (x) dx
2
2
2
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