Question

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]

Answer #1

Let f(x)=2x^3 - 9x^2 +12x -4
Find the intervals of which f is increasing or decreasing
Find the local maximum and minimum values of f
Find the intervals of concavity and the inflection points

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

4. Given the function y = f(x) = 2x^3 + 3x^2 – 12x +
2
a. Find the intervals where f is increasing/f is
decreasing
b. Find the intervals where f is concave up/f is concave
down
c. Find all relative max and relative min (state which
is which and why)
d. Find all inflection points (also state
why)

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...

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.

Suppose that
f(x)=x−3x^1/3
(A) Find all critical values of f. If there are no critical values,
enter -1000. If there are more than one, enter them separated by
commas.
Critical value(s) =
(B) Use interval notation to indicate where f(x) is
increasing.
Note: When using interval notation in WeBWorK,
you use INF for ∞∞, -INF for
−∞−∞, and U for the union symbol. If there are no
values that satisfy the required condition, then enter "{}" without
the quotation marks....

Find the absolute maximum and minimum values of f(x)=
−x^3−3x^2+4x+3, if any, over the interval
(−∞,+∞)(−∞,+∞).
I know it doesn't have absolute maxima and minima but where do
they occur? In other words x= ? for the maxima and minima?

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) =

6. Let ?(?) be a continuous function defined for all real
numbers, with?'(?)=(?−1)2(?−3)3(?−2)
and
?''(?) = (? − 1)(3? − 7)(2? − 3)(? − 3)2.
On what intervals is ? increasing and decreasing?
Increasing on:
Decreasing on:
Find the x-coordinate(s) of all local minima and maxima of
?.
Local min at x=__________________
Local max at x=_________________
c. On what intervals if ? concave up and concave down?
Concave up on:
Concave down on:
d. Find the x-coordinate(s) of points of...

. Let f(x) = 3x^5/5 −2x^4+1. Find the following:
(a) Interval of increasing:
(b) Interval of decreasing:
(c) Local maximum(s) at x =
d) Local minimum(s) at x =
(e) Interval of concave up:
(f) Interval of concave down:
(g) Inflection point(s) at x =

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