Question

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.

Answer #1

Consider the function f(x) = −x3 + 4x2 + 7x + 1.
(a) Use the first and second derivative tests to determine the
intervals of increase and decrease, the
local maxima and minima, the intervals of concavity, and the
points of inflection.
(b) Use your work in part (a) to compute a suitable table of
x-values and corresponding y-values and carefully sketch the graph
of the function f(x). In your graph, make sure to indicate any
local extrema and any...

1.) Use the second derivative test to find the relative extrema
for f(x) = x4 – x3 - (1/2)x2 + 11. Also find all inflection points,
discuss the concavity of the graph and sketch the graph.

If f(x)-x^3-3x;
a) find the intervals on which f is increasing or
decreasing.
b)find the local maximum and minimum values
c)find the intervals of concavity and inflection points
d)use the information above to sketch and graph of f

Analyze the function f and sketch the curve of f by hand.
Identify the domain, x-intercepts, y-intercepts, asymptotes,
intervals of increasing, intervals of decreasing, local maximums,
local minimums, concavity, and inflection points. f(x) = 3x^4 −
4x^3 + 2

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.

Given the function g(x) = x3-3x + 1, use the first and second
derivative tests to
(a) Find the intervals where g(x) is increasing and
decreasing.
(b) Find the points where the function reaches all realtive
maxima and minima.
(c) Determine the intervals for which g(x) is concave up and
concave down.
(d) Determine all points of inflection for g(x).
(e) Graph g(x). Label your axes, extrema, and point(s) of
inflection.

1) Use the First Derivative Test to find the local maximum and
minimum values of the function. (Enter your answers as a
comma-separated list. If an answer does not exist, enter DNE.):
g(u) = 0.3u3 + 1.8u2 + 146
a)
local minimum values:
b)
local maximum values:
2) Consider the following:
f(x) = x4 − 32x2 + 6
(a) Find the intervals on which f is increasing or
decreasing. (Enter your answers using interval notation.)
increasing:
decreasing:...

Question 1
With: ?(?) = ?3 + 4 ?2
What is the domain of ??
Find the equations of all the asymptotes of ? (if any) (at the
boundaries/holes of the domain)
Find the intercepts of ? (if any)
Is the function even? Odd? If yes, what symmetry will the graph
possess?
Do a sign chart of the first derivative, indicate the intervals
where ? is increasing/decreasing, and
find all the horizontal tangents of ? (if any).
Do a sign...

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

Let f (x) = −x^4− 4x^3. (i) Find the intervals of
increase/decrease of f . (ii) Find the local extrema of f (values
and locations). (iii) Determine the intervals of concavity. (iv)
Find the location of the inflection points of f. (v) Sketch the
graph of f

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