MA 3972-MA-Book April 11, 2018 12:11
Take a Diagnostic Exam 21
- The graph of the functiongis shown in the
figure below. Which of the following is true
forgon (a,b)?
I. g is monotonic on (a,b).
II. g′ is continuous on (a,b).
III. g′′>0on(a,b).
a^0 b
g
y
x
- The graph off is shown in the figure below.
If fis twice differentiable, which of the
following statements is true?
010
f
y
x
(A) f(10)< f′(10)<f′′(10)
(B) f′′(10)< f′(10)< f(10)
(C) f′(10)<f(10)<f′′(10)
(D) f′(10)<f′′(10)< f(10)
- The graph off′, the derivative off, is shown
in the following figure. At what value(s) ofx
is the graph of fconcave up?
x 1 0 x 2 x 3 x 4
y
x
f′
- How many points of inflection does the graph
ofy=sin(x^2 ) have on the interval [−π, π]?
ab^0
f(t)
y
t
- Ifg(x)=
∫x
a
f(t)dtand the graph offis
shown above, which of the graphs below is a
possible graph ofg?
a^0 b
y
x
ab 0
y
x
a
0
b
y
x
(A)
(D)
(B)
ab 0
y
x
(C)
