Math 131 Exam 3 Review
1. Use a differential to approximate a) 
b) 
c) 
2. Find the absolute max and absolute min of 
on the interval
a) [ -2, 0 ] b) [ -2, 4 ]
3. Does the function 
have an
absolute max on [ -1, 2 ]? Does it have an absolute min on
[ -1, 2 ]?
4. Assuming f" is continuous, what can be concluded, if anything, about the graph of f at each x value in the table?
x 0 1 2 3 4
f '(x) 1 -1 0 0 0
f"(x) 2 0 0 1 -1
5. An object travels along a horizontal line forward and backward. s(t) is the position at time t.
What can be said, if anything, about s(t) in each case?
a) The object is momentarily stopped at t=2 seconds and is accelerating.
b) The object is momentarily stopped at t=3 seconds and is decelerating.
c) The object is momentarily stopped at t=4 seconds and acceleration is 0.
6. A certain car gets more miles per gallon of gas as the speed increases. Let
f(v)=miles per gallon at speed v. a) If f"(v) = .01 and f'(0)=0 and f(1)=20.005, find f(v).
b) Let g(v) = v/f(v) which is the gallons per hour the car uses at speed v.
Find the minimum of g(v) and show it is a minimum.
7. A rectangular storage container with an open top is to have a volume of 36 cubic meters. The length of its base is twice the width. Find the dimensions that minimize the surface area.
8. Find the left and right hand Riemann sums for each function on the given interval for the given n.
a) f(x) = sin x
on [ 0, π/2 ] n = 3
sin 0 = 0, sin (π/6)= 1/2
, sin(π/3) = 
/2 , sin(π/2) = 1
b) 
on [ 1, 3 ]
n=3
c) on [ 1, 3
] n=4
9. Use symmetry, geometry or the given info to evaluate each integral.
a) 
b) 
c) 
d)
where f(x) is
the function in 9c) and 
10. Find the function f(t) that meets the given conditions.
a) f"(t)=cos t f(0)=1 and f(π) = π +1
b) 
11. Find each antiderivative.
12. Find each antiderivative.
13. Evaluate using the FTC
14. Evaluate each and compare.
a) 
and 
b)
and 