Question

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.

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) + 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...

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

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

Givenf(x)=x3−6x2+15
(a) Find the critical numbers of f.
(b) Find the open intervals on which the function is increasing
or decreasing.
(c) Apply the First Derivative Test to identify all relative
extrema (that is, all relative minimums and maximums).

Let f(x)=sin x-cos x,0≤x≤2π
Find all inflation point(s) of f.
Find all interval(s) on which f is concave downward.

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...

Use Calculus to find the open intervals on [0, 2pi) for which
the function f(x) = cos x - sin2 x is increasing or
decreasing. Identify any local extrema, specifying the coordinates
of each point.

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