Question

**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)

Answer #1

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...

Find the open interval(s) on which the function is increasing
and decreasing.
Identify the function's local and absolute extreme values, if
any, saying where they occur.
If the function has extreme values, which of the extreme
values, if any, are absolute?
h(x)= x3-4x2

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

For the function below, find a) the open intervals
where the function is increasing b) the open intervals where it is
decreasing, and c) the extreme points.
G(x)=x^10e^x-6

consider the function f(x) = x/1-x^2
(a) Find the open intervals on which f is increasing or
decreasing. Determine any local minimum and maximum values of the
function. Hint: f'(x) = x^2+1/(x^2-1)^2.
(b) Find the open intervals on which the graph of f is concave
upward or concave downward. Determine any inflection points. Hint
f''(x) = -(2x(x^2+3))/(x^2-1)^3.

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 f(x) = 2x4 - 4x2 + 1 find the open
intervals in which the function is increasing and decreasing.
Find open intervals where the function is concave up and concave
down.
Sketch the graph of the function - label all local maximums, all
local minimums, and any inflection points.

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 _______________

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.

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

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