Question

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.

Answer #1

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 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...

1.Find all solutions on the interval [0, 2π)
csc (2x)-9=0
2. Rewrite in terms of sin(x) and cos(x)
Sin (x +11pi/6)

1) find the
absolute extrema of function f(x) = 2 sin x + cos 2x on the
interval [0, 2pi]
2)
is f(x) = tanx
concave up or concave down at x = phi / 6

Let Θ ∼ Unif.([0, 2π]) and consider X = cos(Θ) and Y =
sin(Θ).
Can you find E[X], E[Y], and E[XY]?
clearly, x and y are not independent
I think E[X] = E[Y] = 0 but how do you find E[XY]?

Find the dimension of the subspace U = span {1,sin^2(θ), cos 2θ}
of F[0, 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...

1) In the interval [0,2π) find all the solutions possible (in
radians ) :
a) sin(x)= √3/2
b) √3 cot(x)= -1
c) cos ^2 (x) =-cos(x)
2)The following exercises show a method of solving an equation
of the form: sin( AxB C + ) = , for 0 ≤ x < 2π . Find ALL
solutions .
d) sin(3x) = - 1/2
e) sin(x + π/4) = - √2 /2
f) sin(x/2 - π/3) = 1/2

1. Find the critical numbers of f=sin(x)-cos(x) at interval
[0,?].
If there is more more than one enter them as a comma separated
list. ?=
The maximum value of f on the interval is y=
2. Find the critical numbers of the function f(x)=
x1/6-x-5/6 x=

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