Question

Consider the function below. (If an answer does not exist, enter DNE.)

f(x) = 1/2x^(4) − 4x^(2) + 3

(a)

Find the interval of increase. (Enter your answer using interval notation.)

Find the interval of decrease. (Enter your answer using interval notation.)

(b)

Find the local minimum value(s). (Enter your answers as a comma-separated list.)

Find the local maximum value(s). (Enter your answers as a comma-separated list.)

(c)

Find the inflection points.

(x, y) = (smaller x-value)

(x, y) = (larger x-value)

Find the interval where the graph is concave upward. (Enter your answer using interval notation.)

Find the interval where the graph is concave downward. (Enter your answer using interval notation.)

(d)

Use the information from parts (a)-(c) to sketch the graph. Check your work with a graphing device if you have one.

Answer #1

Let us solve.

Consider the function below. (If an answer does not exist, enter
DNE.)
g(x) = 250 +
8x3 +
x4
(a) Find the interval of increase. (Enter your answer using
interval notation.)
Find the interval of decrease. (Enter your answer using interval
notation.)
(b) Find the local minimum value(s). (Enter your answers as a
comma-separated list.)
Find the local maximum value(s). (Enter your answers as a
comma-separated list.)
(c) Find the inflection points.
(x, y)=(smaller x-value)
(x, y)=(larger x-value)
Find the...

Consider the function below. (If an answer does not exist, enter
DNE.)
h(x) = (x
+ 1)9 − 9x − 3
(a) Find the interval of increase. (Enter your answer using
interval notation.)
Find the interval of decrease. (Enter your answer using interval
notation.)
(b) Find the local minimum value(s). (Enter your answers as a
comma-separated list.)
Find the local maximum value(s). (Enter your answers as a
comma-separated list.)
(c) Find the inflection point.
(x, y) =
Find the interval...

Consider the following. (If an answer does not exist, enter
DNE.)
f '(x) =
x2 + x − 30
(a)
Find the open intervals on which f ′(x) is
increasing or decreasing. (Enter your answers using interval
notation.)
increasing
(−12,∞)
decreasing
(−∞,−12)
(b)
Find the open intervals on which the graph of f is
concave upward or concave downward. (Enter your answers using
interval notation.)
concave upward
concave downward
(c)
Find the x-values of the relative extrema of
f. (Enter...

Consider the following function. (If an answer does not exist,
enter DNE.)
f(x) = 1 +
5
x
−
3
x2
(c) Find the local maximum and minimum values.
(d) Find the interval where the function is concave up. (Enter your
answer using interval notation.)
(e) Find the interval where the function is concave down. (Enter
your answer using interval notation.)
(f) Find the inflection point.
(x, y) =

Consider the equation below. (If an answer does not exist,
enter DNE.)
f(x) = x^4− 50x^2 + 7
(a) Find the interval on which f is increasing. (Enter your
answer using interval notation.)
Find the interval on which f is decreasing. (Enter your answer
using interval notation.)
(b) Find the local minimum and maximum values of f.
local minimum value
local maximum value
(c) Find the inflection points.
(x, y) =
(smaller x-value)
(x, y) =
...

Consider the equation below. (If an answer does not exist,
enter DNE.)
f(x) = x^7ln(x)
(a) Find the interval on which f is increasing. (Enter your
answer using interval notation.)
Find the interval on which f is decreasing. (Enter your answer
using interval notation.)
(b) Find the local minimum and maximum values of f.
local minimum value
local maximum value
(c) Find the inflection point.
(x, y) =
Find the interval on which f is concave up....

Consider the equation below. (If an answer does not exist, enter
DNE.)
f(x) =
x4 − 8x2
+ 7
(b) Find the local minimum and maximum values of f.
(c) Find the interval on which f is concave up. (Enter
your answer using interval notation.)
(d) Find the interval on which f is concave down.(Enter
your answer using interval notation.)

Consider the function below.
f(x) = 7 + 4x2 − x4
(a) Find the interval of increase. (Enter your answer using
interval notation.)
(b) Find the interval of decrease. (Enter your answer using
interval notation.)
(c) Find the local minimum value(s). (Enter your answers as a
comma-separated list. If an answer does not exist, enter DNE.)
(d) Find the local maximum value(s). (Enter your answers as a
comma-separated list. If an answer does not exist, enter DNE.)

Consider the following: y = 3x2-6x+1
a.) Find the interval(s) of increase. Find the
interval(s) of decrease.
b.) Find the local maximum and minimum values. (Enter
your answers as a comma-separated list. If an answer does not
exist, enter DNE.)
c.) Find the interval(s) where the function is concave up. Find
the interval(s) where the function is concave down. Find the
inflection points. (If an answer does not exist, enter DNE.)
d.) Determine the end behavior of the graph.
e.) Use the...

Consider the following. f(x) = 4x3 − 6x2 − 24x + 4
(a) Find the intervals on which f is increasing or decreasing.
(Enter your answers using interval notation.) increasing
decreasing
(b) Find the local maximum and minimum values of f. (If an
answer does not exist, enter DNE.) local minimum value local
maximum value
(c) Find the intervals of concavity and the inflection points.
(Enter your answers using interval notation.)
concave up concave down inflection point (x, y) =

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