Question

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.

Answer #1

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

f(x)=x^3-4x^2+5x-2
Find all critical numbers of the function, then use the second
derivative test on each critical number to determine if it is a
local maximum or minimum. Show your work.

what does a derivative tell us?
F(x)=2x^2-5x-3, [-3,-1]
F(x)=x^2+2x-1, [0,1]
Give the intervals where the function is increasing or
decreasing?
Identify the local maxima and minima
Identify concavity and inflection points

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)= 1/3x^3-3x2+8x+1 Fin the following:
a) f'(x)
b) The critical numbers
c) State the intervals where the function is increasing and
decreasing. You must state the test values that you are
using but don't have to show plugging the test values into the
corresponding function.
d) State the relative maximum and relative minimum, if any.
If there is no relative maximum and/or relative minimum,
then state none. Round the y-value(s) to 2 decimal places, if
needed.

Analyze and plot the graph of f(x)= x^4/2 - 2x^3/3. for this,
find;
1) domain of f:
2)Vertical asymptotes:
3) Horizontal asymptotes:
4) Intersection in y:
5) intersection in x:
6) Critical numbers
7) intervals where f is increasing:
8) Intervals where f is decreasing:
9) Relatives extremes
Relatives minimums:
Relatives maximums:
10) Inflection points:
11) Intervals where f is concave upwards:
12) intervals where f is concave down:
13) plot the graph of f on the plane:

consider the function
f(x)=3x-5/sqrt x^2+1. given f'(x)=5x+3/(x^2+1)^3/2 and
f''(x)=-10x^2-9x+5/(x^2+1)^5/2
a) find the local maximum and minimum values. Justify your
answer using the first or second derivative test . round your
answers to the nearest tenth as needed.
b)find the intervals of concavity and any inflection points of
f. Round to the nearest tenth as needed.
c)graph f(x) and label each important part (domain, x- and y-
intercepts, VA/HA, CN, Increasing/decreasing, local min/max values,
intervals of concavity/ inflection points of f?

Graph the quadratic function f x( ) = −2x 2 + 6x − 3. Give the
vertex, axis, x-intercepts, y-intercept, domain, range, and
intervals of the domain for which the function 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)

For the questions below, consider the following function.
f (x) = 3x^4 - 8x^3 + 6x^2
(a) Find the critical point(s) of f.
(b) Determine the intervals on which f is increasing or
decreasing.
(c) Determine the intervals on which f is concave up or concave
down.
(d) Determine whether each critical point is a local maximum, a
local minimum, or neither.

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