Math 131 In Class Exam 3 Review
1. Use a differential to approximate : 
2. Find the absolute max and absolute min of 
on the interval [ -2,
3 ].
3. Does 
have an absolute max
or an absolute min on the given interval? If so, find it.
a) [ -1, 1] b) [1, 3 ]
4. Assuming f " is continuous, what can be concluded about f at each x-value?
x | -1 0 1 2 3
f '(x)| 2 3 0 0 0
f "(x)| 0 -1 1 0 -2
5. An object is traveling back and forth on a straight path. What can be concluded in each case about the distance from start?
a) the object is stopped instantaneously but is accelerating.
b) the object is stopped instantaneously but is decelerating.
6. 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.
7. Write out but do not compute the left and right hand
Riemann sums for 
on [0, 2] with n = 5.
8. Evaluate using geometry or symmetry.
b) 
c) 
9. Find the function, f(t), for which 
10. Find each antiderivative.
dt
11. Find each antiderivative.
12. Evaluate each integral.
13. Simplify each to a function of x without derivatives or integrals.
a) 
b) 