Question

Let f(x) = 3x^{5} − 40x^{3} .

(a) (2 pt) Find f^{'}(x) and f^{"}(x)

(b) (2 pts) Solve for the intervals where the function is concave down and concave up.

(c) (2 pts) Find the absolute maximum and minimum, if they exist. Explain your reasoning

Answer #1

Let f (x) = 3x^4 −4x^3 −12x^2 + 1, deﬁned on R.
(a) Find the intervals where f is increasing, and decreasing.
(b) Find the intervals where f is concave up, and concave
down.
(c) Find the local maxima, the local minima, and the points of
inflection.
(d) Find the Maximum and Minimum Absolute of f over [−2.3]

Let f(x) = (x2 + 3x + 1)e-x .
(a) (1 pt) Find f'
(x)
(b) (3 pts) Solve for the intervals of increase and decrease.
Show your work.
(c) (2 pts) Find any local maxima or minima, and where they
occur

Let
f(x)=((x+1)^2)/((x−1)^2)
(a) (8 pts) Find the intervals on which
f
increases and the intervals on which f decreases. Find
all the local maximum and minimum values of f
.
(b) Find the intervals on which f
is concave upward and concave downward. Find the inflection
points.

Let f(x) = x3 + 3x2 - 24x - 10
a) Find the intervals on which f is increasing/decreasing, and
find all local maximum and local minimum values of f.
b) Find all intervals on which f is concave up/concave down, and
find all inflection points of f.

given function f(x)=-x^3+5x^2-3x+2
A) Determine the intervals where F(x) Is increasing and
decreasing
b) use your answer from a to determine any relative maxima or
minima of the function
c) Find that intervals where f(x) is concave up and concave
down and any points of inflection

Consider the following. f(x) = 4x3 − 6x2 − 24x + 4
(a) Find the intervals on which f is increasing or decreasing.
(Enter your answers using interval notation.) increasing
decreasing
(b) Find the local maximum and minimum values of f. (If an
answer does not exist, enter DNE.) local minimum value local
maximum value
(c) Find the intervals of concavity and the inflection points.
(Enter your answers using interval notation.)
concave up concave down inflection point (x, y) =

Let g (x) = [(x^2-3)/(x^3)]
(a) Determine (if they exist) the vertical and horizontal
asymptotes of g.
(b) Find the formula for g′ (x) and g′′ (x).
(c) Find (if they exist) the local extremes of g.
(d) Find (if they exist) the inflection points of g.
(e) Determine the intervals where g is increasing, and where g
is decreasing.
(f) Determine the intervals where g is concave upward, and
where g is
concave down.
(g) Plot the graph of...

Let f(x)=4+12x−x^3. Find (a) the intervals on which ff is
increasing, (b) the intervals on which ff is decreasing, (c) the
open intervals on which ff is concave up, (d) the open intervals on
which f is concave down, and (e) the x-coordinates of all
inflection points.
(a) f is increasing on the interval(s) =
(b) f is decreasing on the interval(s) =
(c) f is concave up on the open interval(s) =
(d) f is concave down on the...

Consider the following function. (If an answer does not exist,
enter DNE.)
f(x) = 1 +
5
x
−
3
x2
(c) Find the local maximum and minimum values.
(d) Find the interval where the function is concave up. (Enter your
answer using interval notation.)
(e) Find the interval where the function is concave down. (Enter
your answer using interval notation.)
(f) Find the inflection point.
(x, y) =

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.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 3 minutes ago

asked 7 minutes ago

asked 12 minutes ago

asked 13 minutes ago

asked 33 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago