Question

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 (x, y) = Incorrect: Your answer is incorrect. (smaller x-value) (x, y) =

Answer #1

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) =

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.

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...

46. Use Newton's Method to approximate the zero(s) of the
function. Continue the iterations until two successive
approximations differ by less than 0.001. Then find the zero(s) to
three decimal places using a graphing utility and compare the
results.
f(x) = 2 − x3
Newton's method:
Graphing utility:
x =
x =
48. Find the differential dy of the given function.
(Use "dx" for dx.)
y = x+1/3x-5
dy =
49.Find the differential dy of the given function.
y...

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

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
f(x)=
x3
x2 − 4
Express the domain of the function in interval notation:
Find the y-intercept: y=
.
Find all the x-intercepts (enter your answer as a
comma-separated list): x=
.
On which intervals is the function positive?
On which intervals is the function negative?
Does f have any symmetries?
f is even;f is
odd; f is periodic;None of the
above.
Find all the asymptotes of f (enter your answers as
equations):
Vertical asymptote (left):
;
Vertical...

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

For the function f(x)=x^3+5x^2-8x , determine the intervals
where the function is increasing and decreasing and also find any
relative maxima and/or minima. Increasing ____________________
Decreasing ___________________ Relative Maxima _______________
Relative Minima _______________

Consider the function f(x) = x3 − 2x2 − 4x + 9 on the interval
[−1, 3].
Find f '(x). f '(x) = 3x2−4x−4
Find the critical values. x =
Evaluate the function at critical values. (x, y) =
(smaller x-value)
(x, y) =
(larger x-value)
Evaluate the function at the endpoints of the given
interval.
(x, y) =
(smaller x-value)
(x, y) =
(larger x-value)
Find the absolute maxima and minima for f(x) on the interval
[−1, 3].
absolute...

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