Question

A twice-differentiable function, f(x), has a derivative given by f'(x) = (x²-9)g(x), where g(x) < 0 for all values of x. Use this information to answers question #7-10. Show all work and justify your conclusions (up to 5 points each). 7. For what value(s) of x does f(x) have a relative maximum? Justify. 8. For what value(s) of x does f(x) have a relative minimum? Justify. 9. On what interval(s) of x is f(x) increasing? Justify. 10. On what interval(s) of x is f(x) decreasing? Justify. Use the table of values given for a twice-differentiable function shown below to answer questions 11 through 14 (up to 5 points each). X x < -2 x=-2 -2<x<1 x=1 1<x<3 x=3 x>3 f'(x) Pos 0 Neg 0 Neg 0 Pos f"(x) Neg Neg Neg 0 Pos Pos Pos 11. For what value(s) of x does f(x) have relative extrema? Specify the type and justify. 12. For what value(s) of x does f(x) have any points of inflection? Justify. 13. State the intervals of x where f(x) is increasing and where f(x) is decreasing. Justify. 14. Describe the concavity of f(x) at different intervals of x. Justify.

          A twice-differentiable function, f(x), has a derivative given by f'(x) = (x²-9)g(x), where
g(x) < 0 for all values of x. Use this information to answers question #7-10. Show all work
and justify your conclusions (up to 5 points each).
7. For what value(s) of x does f(x)
have a relative maximum? Justify.
8. For what value(s) of x does f(x) have
a relative minimum? Justify.
9. On what interval(s) of x is f(x)
increasing? Justify.
10. On what interval(s) of x is f(x)
decreasing? Justify.
Use the table of values given for a twice-differentiable function shown below to
answer questions 11 through 14 (up to 5 points each).
X
x < -2
x=-2 -2<x<1
x=1 1<x<3
x=3
x>3
f'(x)
Pos
0
Neg
0
Neg
0
Pos
f"(x)
Neg
Neg
Neg
0
Pos
Pos
Pos
11. For what value(s) of x does f(x) have
relative extrema? Specify the type
and justify.
12. For what value(s) of x does f(x) have
any points of inflection? Justify.
13. State the intervals of x where f(x) is
increasing and where f(x) is
decreasing. Justify.
14. Describe the concavity of f(x) at
different intervals of x. Justify.

A twice-differentiable function, f(x), has a derivative given by f'(x) = (x²-9)g(x), where
g(x) < 0 for all values of x. Use this information to answers question #7-10. Show all work
and justify your conclusions (up to 5 points each).
7. For what value(s) of x does f(x)
have a relative maximum? Justify.
8. For what value(s) of x does f(x) have
a relative minimum? Justify.
9. On what interval(s) of x is f(x)
increasing? Justify.
10. On what interval(s) of x is f(x)
decreasing? Justify.
Use the table of values given for a twice-differentiable function shown below to
answer questions 11 through 14 (up to 5 points each).
X
x < -2
x=-2 -2<x<1
x=1 1<x<3
x=3
x>3
f'(x)
Pos
0
Neg
0
Neg
0
Pos
f"(x)
Neg
Neg
Neg
0
Pos
Pos
Pos
11. For what value(s) of x does f(x) have
relative extrema? Specify the type
and justify.
12. For what value(s) of x does f(x) have
any points of inflection? Justify.
13. State the intervals of x where f(x) is
increasing and where f(x) is
decreasing. Justify.
14. Describe the concavity of f(x) at
different intervals of x. Justify.

Added by Teresa M.

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