Question

f(x)= x^4-2x^2-3. Using the first derivative test, find:

a. All critical Numbers

b. Intervals on which f(x) is increasing or decreasing

c. location and value of all relative extrema

Answer #1

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).

f(x)=5x^(2/3)-2x^(5/3)
a. Give the domain of f
b. Find the critical numbers of f
c. Create a number line to determine the intervals on which f is
increasing and decreasing.
d. Use the First Derivative Test to determine whether each
critical point corresponds to a relative maximum, minimum, or
neither.

Find all critical numbers, the open intervals on which f(x) is
increasing or decreasing, and locate and classify all relative
extrema.
f (x) = x3- 13/2
x2- 10x + 7
and
f (x)= x1/3 (x-4)

a) Find all x- values of the critical values and relative
extrema. Then find
the intervals where the graph is increasing and decreasing.
f(x)= (2/3)x^3+x^2
A) Relative Max: _________________________ B) Relative Min:
__________________________
C) Critical Values: ________________________ D) Increasing
Intervals: ___________________
E) Decreasing Intervals: _____________________
(Please show all work as much as possible)

Let f(x)=6x^2−2x^4. Find the open intervals on which f is
increasing (decreasing). Then determine the x-coordinates of all
relative maxima (minima).
1.
f is increasing on the intervals
2.
f is decreasing on the intervals
3.
The relative maxima of f occur at x =
4.
The relative minima of f occur at x =

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...

For f(x) xe-x
( a) Find the local extrema by hand using the first derivative
and a sign chart. b) Find the open intervals where the function is
increasing and where it is decreasing. c) Find the intervals of
concavity and inflection points by hand. d) Sketch a reasonable
graph showing all this behavior . Indicate the coordinates of the
local extrema and inflections.

Find all local extrema and the intervals on which
f(x)=x+sin(2x), considered on the interval (-pi/2,pi/2) is
increasing or decreasing.?

Given the function
h(x)=e^-x^2
Find first derivative f ‘ and second derivative
f''
Find the critical Numbers and determine the intervals
where h(x) is increasing and decreasing.
Find the point of inflection (if it exists) and determine
the intervals where h(x) concaves up and concaves
down.
Find the local Max/Min (including the
y-coordinate)

Find the intervals on which f(x) is increasing, the intervals
on which f(x) is decreasing, and the local extrema. f(x)=
-2x^2-20x-21

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