Question

Answer the following questions for the function

f(x)=x√x2+1f(x)=xx2+1

defined on the interval −5≤x≤7-5≤x≤7.

f(x)f(x) is concave down on the interval *x*
= to *x*
=

f(x)f(x) is concave up on the interval *x*
= to *x*
=

The inflection point for this function is at *x*
=

The minimum for this function occurs at *x*
=

The maximum for this function occurs at *x* =

2)

Consider the function
f(x)=12x^{5}+15x^{4}−240x^{3}+7f

f(x) has inflection points at (reading from left to right)
*x* = *D*, *E*, and *F*

where *D* is

and *E* is

and *F* is

Answer #1

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) =

(a) The altitude of a triangle is increasing at a rate of 1
centimeters/minute while the area of the
triangle is increasing at a rate of 2 square centimeters/minute. At
what rate is the base of the
triangle changing when the altitude is 7 centimeters and the area
is 88 square centimeters?
(b) f(x)=x√x^2+1
defined on the interval −5≤x≤6
f(x) is concave down on the interval x = ___ to x
=___
f(x) is concave up on the interval x...

1. (Continued) Consider the function
(e)
(f)
f (x) = x3 − 7 x + 5. 2
(0.5 pt) Find the possible inflection points of f(x). Show
work.
(0.5 pt) Test the possible inflection points of f(x) to
determine if each point is or is not an inflection point. Your work
must show that you tested each point properly and support your
conclusion. Be sure to state your conclusion. Show work.
(g)
(1 pt) Find the global minimum and global...

. 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 =

Consider the function
f(x)=
x3
x2 − 4
Express the domain of the function in interval notation:
Find the y-intercept: y=
.
Find all the x-intercepts (enter your answer as a
comma-separated list): x=
.
On which intervals is the function positive?
On which intervals is the function negative?
Does f have any symmetries?
f is even;f is
odd; f is periodic;None of the
above.
Find all the asymptotes of f (enter your answers as
equations):
Vertical asymptote (left):
;
Vertical...

1, Let f be a function such that f′′(x) =x(x+ 1)(x−2)^2. Find
the open intervals on which is concave up/down.
2. An inflection point is an x-value at which the concavity of a
function changes. For example, if f is concave up to the left of
x=c and f is concave down to the right of x=c, then x=c is an
inflection point. Find all inflection points in the function from
Problem 1.

Let f(x) = 3x^5/5 −2x^4+1 Find the following
-Interval of increasing
-Interval of decreasing
-Local maximum(s) at x =
-Local minimum(s) at x =
-Interval of concave up
-Interval of concave down
-Inflection point(s) at x =

Let f(x) = 3x^5/5 −2x^4+1 Find the following
-Interval of increasing
-Interval of decreasing
-Local maximum(s) at x =
-Local minimum(s) at x =
-Interval of concave up
-Interval of concave down
-Inflection point(s) at x =

f (x) = ex/x2
Find the Domain of f(x)
Does the function have x- or y- intercept of
f(x)?
Find the vertical and horizontal asymptotes.
Find f'(x) and f''(x) .
Find the critical points, find the interval where f(x) is
increasing and decreasing, the interval where f(x) is concave up
and down and the inflection points.

Given a function?(?)= −?5 +5?−10, −2 ≤ ? ≤ 2
(a) Find critical numbers
(b) Find the increasing interval and decreasing interval of
f
(c) Find the local minimum and local maximum values of f
(d) Find the global minimum and global maximum values of f
(e) Find the inflection points
(f) Find the interval on which f is concave up and concave
down
(g) Sketch for function based on the information from part
(a)-(f)

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