16. Find any relative extrema of the function. List each extremum along with the x-value at which it occurs, Identify intervals over which the
function is increasing and over which it is decreasing. Then sketch a graph of the function.
15
6
f(x) = x³ + 6x²
Describe any relative extrema. Select the correct choice below and, if necessary, fill in the answer box(es) within your choice.
A. The relative maximum point(s) is/are
and there are no relative minimum
points.
(Simplify your answer. Type an ordered pair, using integers or fractions. Use a comma to
separate answers as needed.)
B. The relative minimum point(s) is/are
and there are no relative maximum
points.
(Simplify your answer. Type an ordered pair, using integers or fractions. Use a comma to
separate answers as needed.)
C. The relative minimum point(s) is/are
and the relative maximum point(s)
is/are
(Simplify your answers. Type ordered pairs, using integers or fractions. Use a comma to
separate answers as needed.)
OD. There are no relative minimum points and there are no relative maximum points.
Identify any intervals over which the function is increasing or decreasing. Select the correct choice below and fill in the answer box(es)
within your choice.
A. The function f(x) is decreasing over the interval(s)
and is not increasing
anywhere.
(Type your answer in interval notation. Use integers or fractions for any numbers in the
expression. Use a comma to separate answers as needed.)
B. The function f(x) is increasing over the interval(s)
and decreasing over
the interval(s)
(Type your answers in interval notation. Use integers or fractions for any numbers in the
expressions. Use a comma to separate answers as needed.)
C. The function f(x) is increasing over the interval(s)
and is not decreasing
anywhere.
(Type your answer in interval notation. Use integers or fractions for any numbers in the
expression. Use a comma to separate answers as needed.)
Choose the correct graph below.
OA.
B.
Oc.
OD.
Ay
