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.

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]?

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=

Suppose you know that f′(x) = x sin(2x) − sin(2x). Find the
x-coordinates of all local maximums of f in the interval (0,
2π).

1, Solve cos(x)=0.17cos(x)=0.17 on 0≤x<2π0≤x<2π
There are two solutions, A and B, with A < B
2, Find the EXACT value of cos(A−B)cos(A-B) if sin A = 3434, cos
A = √7474, sin B = √91109110, and cos B = 310310.
cos(A−B)cos(A-B) =
3,
Find all solutions of the equation 2cosx−1=02cosx-1=0 on
0≤x<2π0≤x<2π
The answers are A and B, where A<BA<B
A=? B=?

With the parametric equation x=cos(t)+tsin(t), y=sin(t)-tcos(t)
, 0 ≤ t ≤ 2π)
Find the length of the given curve. (10 point)
2) In the circle of r = 6, the area
above the r = 3 cos (θ) line
Write the integral or integrals expressing the area of this
region by drawing. (10 point)

Let f(x) = 3x^5/5 −2x^4+1 Find the following
-Interval of increasing
-Interval of decreasing
-Local maximum(s) at x =
-Local minimum(s) at x =
-Interval of concave up
-Interval of concave down
-Inflection point(s) at x =

Let f(x) = 3x^5/5 −2x^4+1 Find the following
-Interval of increasing
-Interval of decreasing
-Local maximum(s) at x =
-Local minimum(s) at x =
-Interval of concave up
-Interval of concave down
-Inflection point(s) at x =

Find f.
a. f '''(x) = cos x, f(0) = 1, f '(0) = 4, f ''(0) = 3
b. f''(x) = sin(x) + cos (x), f(0) = 1, f'(0) = 3.

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