Question

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

Answer #1

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

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) =

3. Determine the open intervals on which each function is
increasing / decreasing and identify all relative minimum and
relative maximum for one of the following functions (your
choice).
a) f(x) = sinx + cosx on the interval (0,2π)
b) f(x)=x5-5x/5

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...

a. Find the open intervals on which the
function is increasing and decreasing.
b. Identify the function's local and absolute
extreme values, if any, saying where they occur.
f(x)= x^3/(5x^2+2)

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.

a. Find the open interval(s) on which the function is
increasing and decreasing.
b. Identify the function's local and absolute extreme values,
if any, saying where they occur.
g(t) = -2t^2 + 3t -4
a. Find the open intervals on which the function is
increasing.
Find the open intervals on which the function is
decreasing.
b. Find each local maximum, if there are any.
Find each local minimum, if there are any.
If the function has extreme values, which of...

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)

Consider the function on the interval (0, 2π). f(x) = sin(x)
cos(x) + 2 (a) Find the open interval(s) on which the function is
increasing or decreasing. (Enter your answers using interval
notation.) increasing Incorrect: Your answer is incorrect.
decreasing Incorrect: Your answer is incorrect. (b) Apply the First
Derivative Test to identify all relative extrema. relative maxima
(x, y) = Incorrect: Your answer is incorrect. (smaller x-value) (x,
y) = Incorrect: Your answer is incorrect. (larger x-value) relative
minima...

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

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