BC 1-2
Problem Set #2
Spring 2012
Name
Due Date: Tuesday, 31 Jan. (at beginning of class)
Please show appropriate work – no big calculator leaps – except as indicated. Work should be shown
clearly, using correct mathematical notation. Please show enough work on all problems (unless
specified otherwise) so that others could follow your work and do a similar problem without help.
Collaboration is encouraged, but in the end, the work should be your own.
1.
Sketch the graph of the derivative of f ( x)  x , then find a formula for f ( x ) .
2. Look at the graph of f ( x)  x . Let A( x ) be the function that gives the (signed) area between the
x-axis, the graph of f and the vertical line at x. By signed area we mean that if x  0 , A( x ) is the
opposite of the area between the x-axis, the graph of f and the vertical line at x.
a. Find a formula for A( x ) .
b. Sketch the graphs of A and f on the same set of axes below.
BC 1-2
Problem Set #1 p.1
Spring 2012
BC 1-2
Problem Set #2
Spring 2012
BC 1-2
Name
Due Date: Tuesday, 31 Jan. (at beginning of class)
Problem Set #1 p.2
Spring 2012
3. Given the graph of a velocity function below, sketch the displacement on the same set of axes.
Assume the displacement at t = 0 is 0.
BC 1-2
Problem Set #1 p.3
Spring 2012
4) A tall, thin vase with circular cross sections has cross-sectional area as given below, where the x-axis
represents the height of the vase in inches, and the y-axis is the area of the cross-sectional circle in units of in 2 .
Water is poured into the vase at a rate of 1 in 3 /sec. Create a graph of the height of the water in the vase, in
inches, as a function of time, in seconds. Explain any relevant features of the graph. Label the scales on both
axes; while these will not be exact, the numbers should be reasonable.
y





x












.
BC 1-2
Problem Set #1 p.4
Spring 2012