Question

Find the open intervals on which the function is increasing or
decreasing. (Enter your answers using interval notation. If an
answer does not exist, enter DNE.)

f(x) = sin(x) + cos(x), 0 < x < 2π

Answer #1

Identify the open intervals on which the function is increasing
or decreasing. (Enter your answers using interval notation.)
f(x) = sin(x) + 3 0 < x
< 2π

question #1: Consider the following function.
f(x) =
16 − x2,
x ≤ 0
−7x,
x > 0
(a) Find the critical numbers of f. (Enter your answers
as a comma-separated list.)
x =
(b) Find the open intervals on which the function is increasing or
decreasing. (Enter your answers using interval notation. If an
answer does not exist, enter DNE.)
increasing
decreasing
question#2:
Consider the following function.
f(x) =
2x + 1,
x ≤ −1
x2 − 2,
x...

1. Consider the following.
h(x)=x 3sqrt(x-5)
Find the critical numbers. (Enter your answers as a
comma-separated list. If an answer does not exist, enter DNE.)
x =
Find the open intervals on which the function is increasing or
decreasing. Use a graphing utility to verify your results. (Enter
your answers using interval notation. If an answer does not exist,
enter DNE.)
increasing:
decreasing:
2. Compare the values of dy and Δy for the
function. (Round your answers to four decimal...

Determine the open intervals on which the graph is concave
upward or concave downward. (Enter your answers using interval
notation. If an answer does not exist, enter DNE.)
y = 3x +
2
sin x
, (−π, π)

question number 1:
Find the point of inflection of the graph of the function. (If
an answer does not exist, enter DNE.)
f(x) = x + 7 cos x, [0, 2π]
(x, y)
=
DNE
(smaller x-value)
(x, y)
=
DNE
(larger x-value)
Describe the concavity. (Enter your answers using interval
notation. If an answer does not exist, enter DNE.)
concave upward
DNE
concave downward
question number 2:
Find the points of inflection of the graph of the...

Consider the function on the interval (0, 2π).
f(x) =
sin(x)/
2 + (cos(x))2
(a) Find the open intervals on which the function is increasing
or decreasing. (Enter your answers using interval notation.)
increasing
decreasing
(b) Apply the First Derivative Test to identify the relative
extrema.
relative maximum
(x, y) =
relative minimum
(x, y) =

Determine the open intervals on which the graph is concave
upward or concave downward. (Enter your answers using interval
notation. If an answer does not exist, enter DNE.)
f(x) = x^2+2 / x^2 - 4

Consider the function on the interval (0, 2π). f(x) = sin(x)
cos(x) + 4. (A) Find the open interval(s) on which the function is
increasing or decreasing. (Enter your answers using interval
notation.) (B) Apply the First Derivative Test to identify all
relative extrema.

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) =

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...

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