Question

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 the extreme values, if any, are absolute?

Answer #1

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

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)

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

Find a. intervals on which the function is increasing or
decreasing. b. the local maximum and minimum values of the
function. c. the intervals of concavity and the inflection points.
h(θ) = sin(2θ)/1 + cos(θ)

) Let
.f'(x)=x2-4x-5
Determine the interval(s) of x for which the function
is increasing, and the interval(s) for which the function is
decreasing.
Find the local extreme values of f(x) , specifying
whether each value is a local maximum value or a local minimum
value of f.
Graph a sketch of the graph with parts (a) and (b) labeled

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

The function
f(x)=−6x3−6.93x2+52.7724x−2.19f(x)
is increasing on the open interval
( , ).
It is decreasing on the open interval ( −∞, ) and the
open interval ( , ∞ ).
The function has a local maximum at .
Question #2
The function f(x)=3x+9x−1 has one local minimum and one local
maximum.
This function has a local maximum at x=
with value
and a local minimum at x=
with value

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

a) Find the intervals over which f is increasing or
decreasing.
b) Find the local maximum and minimum values of f.
c) Find the concavity intervals and the inflection points.
?(?)=4x3+3?2−6?+4

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