Wednesday, January 9
Clicker Questions
Clicker Question 1
3
Z
x
Define g(x) =
2
f (t) dt, where
−2
y= f HtL
1
f (t) is the function to the right.
-2
1
-1
2
3
-1
“Net area so far” function
Between x = −2 and x = 3: on what interval, if any, is g(x) flat?
On what interval is g(x) decreasing?
A. g(x) is not flat on any interval, but decreasing for 0 ≤ x ≤ 2
B. g(x) is not flat on any interval, but decreasing for 1 ≤ x ≤ 3
C. g(x) is flat for −1 ≤ x ≤ 0, and decreasing for 0 ≤ x ≤ 2
D. g(x) is flat for −1 ≤ x ≤ 0, and decreasing for 1 ≤ x ≤ 3
E. none of the above
Clicker Question 2
Recalling properties of derivatives
Suppose that f (x) and g(x) are differentiable functions, and
f 0 (x) = g0 (x) for all x. What is the relationship between f and g?
A. f (x) and g(x) are the same
function
B. f (x) and g(x) add to 0
C. f (x) divided by g(x) is a constant
D. f (x) minus g(x) is a constant
E. no relationship, totally random
Clicker Question 3
Head over heels
Suppose that g(x) is defined by
Z
g(x) =
8
f (t) dt
x
(with the variable on the bottom rather than the top). What is
g0 (x) then?
A. g0 (x) = −f (8)
B. g0 (x) = f (8)
C. g0 (x) = −f (x)
D. g0 (x) = f (x)
E. none of the above
Clicker Question 4
Composition of functions
Define h(x) = x3 and
Z
x
g(x) =
5
√
t+2
dt.
−1
What is the composition (g ◦ h)(x) = g(h(x))?
Z
x3
A.
√
5
t+2
dt
−1
Z
x
B.
Z
x
−1
√
C.
D.
√
5
5
t3 +2
Z−1
x √
5
t+2
3
dt
dt
t+2
3
dt
−1
E. none of the above