Group Project 2
Derivatives, Tangent Lines and Rates of Change
Instructions: In your groups discuss each question and come to a consensus on the answer. Once you have agreed on
an answer scratch off the paint for that answer. If you see a ? then your answer is correct. If you do not see a ?,
discuss the question again and try again. Continue until you have uncovered the ?. Each of the five problems is worth
4 points. Your score on each question will be 4 − (# incorrect attempts). Write the names of the group members on
the back of the scratch ticket before you turn it in.
1. Let h be a function with h0 (10) = −12, and let g(x) = h(x2 + 1). Then g 0 (3)
A. cannot be determined.
B. is equal to −72.
C. is equal to −12.
D. is equal to 145.
E. is equal to −120.
2. At the point (0, 0), the graph of the function y = |x|,
A. has exactly one tangent line, y = 0.
B. has exactly two tangent lines, y = x and y = −x.
C. has the vertical line x = 0 s a tangent line.
D. has no tangent line.
E. has infinitely many tangent lines.
3. At the point (0, 0), the graph of the function y = x,
A. has exactly one tangent line, y = 0.
B. has exactly one tangent line, y = x.
C. has exactly two tangent lines, y = x and y = −x.
D. has infinitely many tangent lines.
E. has no tangent line.
4. lim
h→0
sin(2x + h) − sin(2x)
h
A. is equal to 2 cos(2x).
B. is equal to cos(2x).
C. is equal to 1.
D. is equal to 2.
E. does not exist.
5. A slow freight train chugs along a straight track. The distance it has traveled in miles after t hours is given by
the function f (t). An engineer is walking along the top of the box cars at the rate of 3 mi/hr in the direction
opposite to the direction that the train is moving. The speed of the man relative to the ground is
A. f 0 (t) − 3.
B. f 0 (t) + 3.
C. f (t) − 3.
D. f (t) + 3.
E. None of these.