Math 131 In Class Exam 3 Review
J. Lewis
3
f ( x)  x  3x
1. Find the absolute max and absolute min of
e
f (x) 
2. Does
x
find it.
a) [ -1, 1]
2
on the interval [ -2, 3 ].
x
2
have an absolute max or an absolute min on the given interval? If so,
c) (0,  )
b) [1, 3 ]
3. Assuming f " is continuous, what can be concluded about f at each x-value?
x | -1
f '(x)| 2
f "(x)| 0
0
3
-1
1
0
1
2
0
0
3
0
-2
4. Stewart 4.6.14 A storage box with an open top is to have a volume of 10 cubic meters.
The length of the base is twice the width. Material for the base costs $10 per sq.m and
material for the sides costs $6 per sq.m Find the dimensions for the cheapest such box.
5. Write out but do not compute the left and right hand Riemann sums for
a) f ( x )  e on [0, 2] with n = 5.
x
b) f ( x )  4  4 x
x
2
on [0, 2] n=4 Sketch the rectangles.
6. Evaluate using geometry or symmetry.
30
1
 | x | dx
a)
b)
2

9
 2 x  3 x  14 x ) dx
7
5
 30

3
c)
 (x
9  x  4 ( x  3 ) dx
2
0
7. The velocity of an object moving back and forth on a straight path is
v ( t )  20  5 t m/s. The position at t=0 is s(0)=0.
2
a) Find the position at t=3. b) Find the total distance traveled in the first 3 seconds.
8. Find the function, f(t), for which
a) f " ( t )  8 e
2t
b) f " ( x )  6 x  2
f ' (0)  6
f (1)  4
f (0)  3
f ( 2 )  24
9. Evaluate each definite integral.
x2
4

a)
x5
1
1
ln 6
dx

b)
e ( e  3 ) 2 dx
x
x
0
10. Find each antiderivative.

a)
x
g)
 x( x
j)

ln x
2
2
b )  ( 6 e  4 sin t ) dt
t
dx
2 3
 tan
e)
x  2x
3
1
2
t sec t dt
 1) dx
8
dx
x
k)
 sin
f)
h)

x
3
3
c)
1
x (ln x )
2
dx
x
8
x
d 
 sin

dx  1
x
b)
3

t dt 


 dt sin t  dt
1
d
3
2
1 2
i )  e ( 3 e  1) dx
x
dx
11. Simplify each to a function of x without derivatives or integrals.
a)
d )  3 sec t dt
t cos t dt
( x  1) dx
2

x